Algebra 1 Practice Test: Slope-Intercept and Point-Slope Form
- Slope-Intercept and Point-Slope Form
- 10 questions
- 13 minutes
These 10 questions practice y = mx + b and y − y₁ = m(x − x₁). In point-slope form, the signs inside the parentheses are the opposite of the point's coordinates.
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Question 1
Which equation is the point-slope form of the line through (2, 5) with slope 3?
Correct answer: A
Point-slope form is y − y1 = m(x − x1). With (2, 5) and m = 3, that is y − 5 = 3(x − 2). Swapping the coordinates gives y − 2 = 3(x − 5).
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Question 2
Write y − 4 = −2(x + 1) in slope-intercept form.
Correct answer: C
Distribute: y − 4 = −2x − 2. Add 4: y = −2x + 2. Writing −2 · 1 as +2 leads to y = −2x + 6.
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Question 3
Which equation describes the line through (1, 3) and (4, 9)?
Correct answer: D
The slope is 9 − 34 − 1 = 2. Using (1, 3): 3 = 2 + b, so b = 1. Dividing the x-change by the y-change gives the trap slope 12.
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Question 4
What are the slope and the y-intercept of 4x − 2y = 8?
Correct answer: B
Solve for y: −2y = −4x + 8, so y = 2x − 4. Dividing by −2 changes the sign of both terms.
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Question 5
Which line is parallel to y = 3x − 7 and passes through (0, 2)?
Correct answer: A
Parallel lines have equal slopes, so m = 3, and the point (0, 2) gives the y-intercept 2. The slope −13 belongs to a perpendicular line.
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Question 6
Which line passes through (2, 0) and is perpendicular to y = 23x + 1?
Correct answer: C
The perpendicular slope is the negative reciprocal, −32. Then y = −32(x − 2) = −32x + 3. Only changing the sign without flipping gives −23.
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Question 7
A taxi charges a base fare of $3 plus $2 per mile, so the cost is y = 2x + 3 for x miles. How much does a 7-mile ride cost?
Correct answer: B
Substitute x = 7: 2(7) + 3 = 17. Swapping slope and intercept gives 3(7) + 2 = 23.
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Question 8
A line passes through (−3, 4) and has slope −12. What is its y-intercept?
Correct answer: D
From y − 4 = −12(x + 3) we get y = −12x − 32 + 4 = −12x + 52. A sign slip on −32 gives 112.
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Question 9
Which point lies on the line y − 2 = 4(x + 1)?
Correct answer: C
Point-slope form shows the point (−1, 2) directly: substituting gives 0 = 4(0). For (1, −2) the left side is −4 but the right side is 8.
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Question 10
The table shows points on a line. Which equation describes the line?
x 0 2 4 y 5 1 −3 Correct answer: A
When x increases by 2, y decreases by 4, so the slope is −42 = −2. At x = 0, y = 5, which is the y-intercept. Using the change in y alone gives −4.
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