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Quiz: Graphing and Linear Functions

Test your understanding of graphing linear functions, slope, intercepts, and linear equations with these questions.

1. What does the slope of a line represent?

  1. The y-intercept
  2. The x-intercept
  3. The rate of change or steepness
  4. The starting point
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The correct answer is C. Slope measures the rate of change—how much y changes for each unit change in x. It represents the steepness and direction of a line. A positive slope rises left to right, while a negative slope falls. Option A describes where the line crosses the y-axis. Option B is where it crosses the x-axis. Option D is vague and doesn't capture the concept.

Concept Tested: Slope

See: Understanding Slope

2. Find the slope of the line passing through points (2, 3) and (6, 11).

  1. 2
  2. 4
  3. 1/2
  4. 8
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The correct answer is A. Using the slope formula m = (y₂ - y₁)/(x₂ - x₁): m = (11 - 3)/(6 - 2) = 8/4 = 2. This means for every 1 unit increase in x, y increases by 2 units. Option B calculates only the change in x. Option C inverts the fraction. Option D gives only the numerator.

Concept Tested: Slope Formula

See: Slope Formula

3. What is the slope of a horizontal line?

  1. 1
  2. 0
  3. Undefined
  4. -1
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The correct answer is B. A horizontal line has zero slope because there is no vertical change (rise = 0) as you move along the line. The equation is y = c for some constant c. Option C describes a vertical line. Options A and D would represent diagonal lines.

Concept Tested: Slope of Horizontal and Vertical Lines

See: Special Cases

4. In the equation y = -3x + 7, what is the y-intercept?

  1. -3
  2. 3
  3. 7
  4. (0, 7)
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The correct answer is C (or D if asking for the point). In slope-intercept form y = mx + b, the b value is the y-intercept, which is 7. This is where the line crosses the y-axis. As a point, it's (0, 7). Option A gives the slope. Option B is the absolute value of the slope.

Concept Tested: Y-Intercept / Slope-Intercept Form

See: Slope-Intercept Form

5. Which form of a linear equation is Ax + By = C?

  1. Slope-intercept form
  2. Point-slope form
  3. Standard form
  4. Vertex form
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The correct answer is C. Standard form of a linear equation is Ax + By = C, where A, B, and C are integers and A is typically non-negative. Option A is y = mx + b. Option B is y - y₁ = m(x - x₁). Option D is for quadratic equations, not linear.

Concept Tested: Standard Form

See: Standard Form

6. What are parallel lines characterized by?

  1. Equal y-intercepts
  2. Equal slopes
  3. Perpendicular intersection
  4. Opposite reciprocal slopes
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The correct answer is B. Parallel lines have equal slopes but different y-intercepts. They never intersect because they rise and run at the same rate. Option A alone doesn't guarantee parallel lines (they could be the same line). Option C describes perpendicular lines. Option D also describes perpendicular lines.

Concept Tested: Parallel Lines

See: Parallel and Perpendicular Lines

7. If a line has slope 2/3, what is the slope of a line perpendicular to it?

  1. 2/3
  2. -2/3
  3. 3/2
  4. -3/2
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The correct answer is D. Perpendicular lines have slopes that are opposite reciprocals. The reciprocal of 2/3 is 3/2, and the opposite (negative) of that is -3/2. When you multiply the slopes of perpendicular lines, you get -1: (2/3) × (-3/2) = -1. Option A is for parallel lines. Option B is just the opposite. Option C is just the reciprocal.

Concept Tested: Perpendicular Lines

See: Parallel and Perpendicular Lines

8. Write the equation of a line with slope 4 passing through point (1, 5).

  1. y = 4x + 1
  2. y - 5 = 4(x - 1)
  3. y = 4x + 5
  4. y - 1 = 4(x - 5)
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The correct answer is B. Using point-slope form y - y₁ = m(x - x₁) with m = 4 and point (1, 5): y - 5 = 4(x - 1). This can be simplified to slope-intercept form: y = 4x + 1. So option A is also correct after simplification. Option C uses the wrong y-intercept. Option D reverses the coordinates.

Concept Tested: Point-Slope Form / Writing Linear Equations

See: Point-Slope Form

9. What is the x-intercept of the line 2x - 3y = 12?

  1. (6, 0)
  2. (0, -4)
  3. (4, 0)
  4. (0, 6)
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The correct answer is A. To find the x-intercept, set y = 0: 2x - 3(0) = 12, so 2x = 12, giving x = 6. The x-intercept is the point (6, 0). Option B is the y-intercept. Options C and D have incorrect calculations.

Concept Tested: X-Intercept / Intercepts

See: Finding Intercepts

10. A linear function models the cost C of renting a car for d days: C = 45d + 25. What does the 25 represent?

  1. The daily rental rate
  2. The total cost for one day
  3. The initial fee (y-intercept)
  4. The number of days
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The correct answer is C. In the equation C = 45d + 25, the constant term 25 is the y-intercept, representing the initial fee or base cost before any days are counted. The 45 is the slope (daily rate). Option A describes the slope. Option B would be 45(1) + 25 = 70. Option D is the variable d.

Concept Tested: Linear Models / Applications

See: Linear Models and Applications