A mathematics problem uses Slope–intercept line. Given slope (m) = 2.4000; x-value (x) = 3.5000; intercept (b) = 10.0000, determine the y-value (y).

Start with the thinking

• The governing relation printed in this handbook section is Slope–intercept line.
• Everything except y is given, so isolate y symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Mathematics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$y = m x + b$$

2. Step 2 — Rearrange the relation so that y stands alone on the left-hand side.

3. Step 3

   $$List the givens: slope (m) = 2.4000, x-value (x) = 3.5000, intercept (b) = 10.0000$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$y = 18.4000$$

6. Step 6 — Check: returning y = 18.4000 to

   $$y = m x + b$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 36.8000 — kept a factor of two that cancels in the correct rearrangement.
• 9.2000 — dropped that same factor in the other direction.
• 20.2400 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Mathematics → Algebra of Complex Numbers

A mathematics problem uses Slope–intercept line. Given x-value (x) = 8.5000; intercept (b) = 7.5000; y-value (y) = 46.8000, determine the slope (m).

Start with the thinking

• The governing relation printed in this handbook section is Slope–intercept line.
• Everything except m is given, so isolate m symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Mathematics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$y = m x + b$$

2. Step 2 — Rearrange the relation so that m stands alone on the left-hand side.

3. Step 3

   $$List the givens: x-value (x) = 8.5000, intercept (b) = 7.5000, y-value (y) = 46.8000$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$m = 4.6235$$

6. Step 6 — Check: returning m = 4.6235 to

   $$y = m x + b$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 9.2471 — kept a factor of two that cancels in the correct rearrangement.
• 2.3118 — dropped that same factor in the other direction.
• 5.0859 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Mathematics → Algebra of Complex Numbers

A mathematics problem uses Slope–intercept line. Given slope (m) = 1.0000; x-value (x) = 7.0000; y-value (y) = 1.6000, determine the intercept (b).

Start with the thinking

• The governing relation printed in this handbook section is Slope–intercept line.
• Everything except b is given, so isolate b symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Mathematics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$y = m x + b$$

2. Step 2 — Rearrange the relation so that b stands alone on the left-hand side.

3. Step 3

   $$List the givens: slope (m) = 1.0000, x-value (x) = 7.0000, y-value (y) = 1.6000$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$b = -5.4000$$

6. Step 6 — Check: returning b = -5.4000 to

   $$y = m x + b$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• -10.8000 — kept a factor of two that cancels in the correct rearrangement.
• -2.7000 — dropped that same factor in the other direction.
• -5.9400 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Mathematics → Algebra of Complex Numbers

A mathematics problem uses Slope–intercept line. Given slope (m) = 4.8000; intercept (b) = -7.5000; y-value (y) = -19.2000, determine the x-value (x).

Start with the thinking

• The governing relation printed in this handbook section is Slope–intercept line.
• Everything except x is given, so isolate x symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Mathematics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$y = m x + b$$

2. Step 2 — Rearrange the relation so that x stands alone on the left-hand side.

3. Step 3

   $$List the givens: slope (m) = 4.8000, intercept (b) = -7.5000, y-value (y) = -19.2000$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$x = -2.4375$$

6. Step 6 — Check: returning x = -2.4375 to

   $$y = m x + b$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• -4.8750 — kept a factor of two that cancels in the correct rearrangement.
• -1.2188 — dropped that same factor in the other direction.
• -2.6813 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Mathematics → Algebra of Complex Numbers

A mathematics problem uses Slope–intercept line. Given slope (m) = 4.3000; x-value (x) = 3.0000; intercept (b) = -7.5000, determine the y-value (y).

Start with the thinking

• The governing relation printed in this handbook section is Slope–intercept line.
• Everything except y is given, so isolate y symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Mathematics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$y = m x + b$$

2. Step 2 — Rearrange the relation so that y stands alone on the left-hand side.

3. Step 3

   $$List the givens: slope (m) = 4.3000, x-value (x) = 3.0000, intercept (b) = -7.5000$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$y = 5.4000$$

6. Step 6 — Check: returning y = 5.4000 to

   $$y = m x + b$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 10.8000 — kept a factor of two that cancels in the correct rearrangement.
• 2.7000 — dropped that same factor in the other direction.
• 5.9400 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Mathematics → Algebra of Complex Numbers

A mathematics problem uses Slope–intercept line. Given x-value (x) = 9.0000; intercept (b) = -0.5000; y-value (y) = 29.8000, determine the slope (m).

Start with the thinking

• The governing relation printed in this handbook section is Slope–intercept line.
• Everything except m is given, so isolate m symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Mathematics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$y = m x + b$$

2. Step 2 — Rearrange the relation so that m stands alone on the left-hand side.

3. Step 3

   $$List the givens: x-value (x) = 9.0000, intercept (b) = -0.5000, y-value (y) = 29.8000$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$m = 3.3667$$

6. Step 6 — Check: returning m = 3.3667 to

   $$y = m x + b$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 6.7333 — kept a factor of two that cancels in the correct rearrangement.
• 1.6833 — dropped that same factor in the other direction.
• 3.7033 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Mathematics → Algebra of Complex Numbers

A mathematics problem uses Slope–intercept line. Given slope (m) = 3.3000; x-value (x) = 9.5000; y-value (y) = -12.2000, determine the intercept (b).

Start with the thinking

• The governing relation printed in this handbook section is Slope–intercept line.
• Everything except b is given, so isolate b symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Mathematics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$y = m x + b$$

2. Step 2 — Rearrange the relation so that b stands alone on the left-hand side.

3. Step 3

   $$List the givens: slope (m) = 3.3000, x-value (x) = 9.5000, y-value (y) = -12.2000$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$b = -43.5500$$

6. Step 6 — Check: returning b = -43.5500 to

   $$y = m x + b$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• -87.1000 — kept a factor of two that cancels in the correct rearrangement.
• -21.7750 — dropped that same factor in the other direction.
• -47.9050 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Mathematics → Algebra of Complex Numbers

A mathematics problem uses Slope–intercept line. Given slope (m) = 4.8000; intercept (b) = 5.5000; y-value (y) = 9.7000, determine the x-value (x).

Start with the thinking

• The governing relation printed in this handbook section is Slope–intercept line.
• Everything except x is given, so isolate x symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Mathematics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$y = m x + b$$

2. Step 2 — Rearrange the relation so that x stands alone on the left-hand side.

3. Step 3

   $$List the givens: slope (m) = 4.8000, intercept (b) = 5.5000, y-value (y) = 9.7000$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$x = 0.8750$$

6. Step 6 — Check: returning x = 0.8750 to

   $$y = m x + b$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 1.7500 — kept a factor of two that cancels in the correct rearrangement.
• 0.4375 — dropped that same factor in the other direction.
• 0.9625 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Mathematics → Algebra of Complex Numbers

A mathematics problem uses Slope–intercept line. Given slope (m) = 2.4000; x-value (x) = 9.0000; intercept (b) = -8.0000, determine the y-value (y).

Start with the thinking

• The governing relation printed in this handbook section is Slope–intercept line.
• Everything except y is given, so isolate y symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Mathematics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$y = m x + b$$

2. Step 2 — Rearrange the relation so that y stands alone on the left-hand side.

3. Step 3

   $$List the givens: slope (m) = 2.4000, x-value (x) = 9.0000, intercept (b) = -8.0000$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$y = 13.6000$$

6. Step 6 — Check: returning y = 13.6000 to

   $$y = m x + b$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 27.2000 — kept a factor of two that cancels in the correct rearrangement.
• 6.8000 — dropped that same factor in the other direction.
• 14.9600 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Mathematics → Algebra of Complex Numbers

A mathematics problem uses Slope–intercept line. Given x-value (x) = 7.0000; intercept (b) = -2.0000; y-value (y) = 23.5000, determine the slope (m).

Start with the thinking

• The governing relation printed in this handbook section is Slope–intercept line.
• Everything except m is given, so isolate m symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Mathematics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$y = m x + b$$

2. Step 2 — Rearrange the relation so that m stands alone on the left-hand side.

3. Step 3

   $$List the givens: x-value (x) = 7.0000, intercept (b) = -2.0000, y-value (y) = 23.5000$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$m = 3.6429$$

6. Step 6 — Check: returning m = 3.6429 to

   $$y = m x + b$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 7.2857 — kept a factor of two that cancels in the correct rearrangement.
• 1.8214 — dropped that same factor in the other direction.
• 4.0071 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Mathematics → Algebra of Complex Numbers