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Quizzes > Mathematics > Algebra

Slope and Slope-Intercept Form Quiz

Sharpen your slope formula skills: take the slope-intercept form quiz now!

Difficulty: Moderate
2-5mins
Learning OutcomesCheat Sheet
Paper cutout quiz graphic about slope intercept form featuring graph lines formulas on dark blue background.

This slope-intercept form quiz helps you practice writing and graphing y = mx + b, find slope, and read lines from a graph. Use it to spot gaps before a test and get instant feedback as you go. Warm up with a quick warm-up or go deeper with line equation practice .

What is the slope-intercept form of a linear equation?
y - b = mx
mx + y = b
y = mx + b
x = my + b
The slope-intercept form is typically written as y = mx + b, where m represents the slope and b represents the y-intercept. It shows directly how much y changes per unit of x and where the line crosses the y-axis. Forms like y - b = mx are related but are actually point-slope or rearranged versions. For more details visit .
Given the equation y = 3x + 2, what is the slope of the line?
2
-3
1/3
3
In the slope-intercept form y = mx + b, the coefficient m is the slope of the line. Here m = 3, so for each 1 unit increase in x, y increases by 3 units. The number 2 in the equation is the y-intercept, not the slope. For more on slope, see .
What is the y-intercept of the line given by y = -4x + 7?
(0, -4)
(0, 7)
(7, 0)
-4
In y = mx + b, b is the y-intercept, and it corresponds to the point (0, b). Here b = 7, so the line crosses the y-axis at (0, 7). The other answers confuse x-intercepts or the slope value. For intercept definitions, visit .
Which of these equations represents a line with positive slope and negative y-intercept?
y = 3x + 2
y = -3x - 2
y = -2x + 3
y = 2x - 3
A positive slope means m > 0 and a negative y-intercept means b < 0 in y = mx + b. Among the options, y = 2x - 3 has m = 2 (positive) and b = -3 (negative). Options with negative slopes or positive intercepts do not meet both criteria. For more examples, see .
What is the equation of the line with slope 2 that passes through the point (0, -5)?
y = -5x + 2
y = 2x + 5
y = 2x - 5
y = 5x + 2
When a line passes through (0, b), b is the y-intercept. Here the point (0, -5) tells us b = -5. Combined with slope m = 2, the equation is y = 2x - 5. The other choices misplace signs or swap x and y. For point applications, visit .
Convert the standard-form equation 2x + 3y = 6 into slope-intercept form.
y = 3/2 x - 2
y = 2/3 x + 6
y = -3/2 x + 6
y = -2/3 x + 2
To convert 2x + 3y = 6, solve for y: 3y = -2x + 6, so y = (-2/3)x + 2. This isolates y and gives slope m = -2/3 and intercept b = 2. Other options result from sign or division errors. For standard-to-slope conversion see .
Find the slope of the line that passes through the points (2, 3) and (5, 11).
3/8
-3/8
-8/3
8/3
Slope is rise over run: (11 - 3) / (5 - 2) = 8 / 3. A negative or reciprocal would indicate different direction or division errors. Always subtract y's and x's in the same order. For slope between points, see .
What is the x-intercept of the line y = (1/2)x + 4?
(-8, 0)
(8, 0)
(0, -8)
(0, 8)
The x-intercept occurs when y = 0. Set 0 = x/2 + 4; solve to get x = -8. Thus the intercept is at (-8, 0). The other points swap coordinates or signs incorrectly. For more, see .
What is the equation in slope-intercept form of the horizontal line that passes through (3, 4)?
y = 0x + 4
y = x + 4
x = 4
y = 4x + 3
A horizontal line has slope 0, so its equation is y = 0x + b. Since it passes through y = 4, b = 4 and the equation is y = 0x + 4 (often simplified to y = 4). The other choices change the slope or treat x as dependent. For horizontal/vertical lines see .
A line perpendicular to y = 2x + 1 passes through (0, -2). What is its equation in slope-intercept form?
y = -2x - 1/2
y = 1/2 x - 2
y = -1/2 x + 2
y = -1/2 x - 2
Perpendicular slopes are negative reciprocals. The original slope is 2, so the perpendicular slope is -1/2. Plugging (0, -2) gives b = -2. Thus the line is y = -1/2 x - 2. The other options either flip signs or miscalculate b. For perpendicular lines see .
Find the slope-intercept form of the line parallel to 3x - y = 6 that passes through the point (2, -1).
y = 3x + 7
y = 3x - 7
y = -3x - 7
y = -3x + 7
Convert 3x - y = 6 to slope-intercept: y = 3x - 6, so the slope is 3. A parallel line has the same slope. Using (2, -1), substitute: -1 = 3·2 + b, so b = -7. Hence y = 3x - 7. For parallels see .
What is the equation of the line passing through (4, -2) and (-1, 3) in slope-intercept form?
y = x + 2
y = x - 2
y = -x + 2
y = -x - 2
Slope m = (3 - (-2)) / (-1 - 4) = 5 / -5 = -1. Use y = mx + b and (4, -2): -2 = -1·4 + b, so b = 2. Therefore y = -x + 2. Other choices miscompute slope or intercept. For more, see .
Write the equation of the line with slope 4 that passes through the point where y = -2x + 8 crosses the x-axis.
y = 4x - 16
y = 4x + 16
y = -4x + 16
y = -4x - 16
The line y = -2x + 8 crosses the x-axis where y = 0: 0 = -2x + 8 ? x = 4. So the point is (4,0). A line with slope 4 through (4,0) gives y = 4x + b and 0 = 4·4 + b ? b = -16. Hence y = 4x - 16. For intercepts see .
Lines 3x - y = 6 and x + 2y = 4 intersect at a point. For what value of b does y = -2/3 x + b pass through their intersection?
y = 3/2 x + 50/21
y = -2/3 x + 32/21
y = -2/3 x + 50/21
y = -2/3 x + 18/21
Solve the system: from 3x - y = 6 ? y = 3x - 6; substitute into x + 2y = 4 ? x + 2(3x - 6) = 4 ? x = 16/7, y = 6/7. Plug into y = -2/3 x + b: 6/7 = -2/3·16/7 + b ? b = 50/21. Other b's come from miscalculation. For systems see .
For the linear function f(x) = ax + b to be tangent to the parabola g(x) = x² at exactly one point, what relationship must a and b satisfy?
b = -4a²
b = -a²/4
b = 4/a²
b = a²/4
A tangent line satisfies both f(x) = g(x) and f?(x) = g?(x) at the touch point x?. Here a = 2x? and x?² = a·x? + b. Substituting gives b = -x?² = -(a/2)² = -a²/4. Thus the condition is b = -a²/4. For calculus-based tangents see .
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Study Outcomes

  1. Apply the Slope Formula -

    Use quiz problems to calculate rise-over-run and determine the slope from two given points accurately.

  2. Interpret Slope-Intercept Form -

    Identify the slope and y-intercept in equations of the form y = mx + b, enhancing your algebra slope-intercept practice skills.

  3. Graph Linear Equations -

    Plot lines on the coordinate plane by applying techniques from the graphing slope intercept form quiz to visualize relationships between variables.

  4. Solve Real-World Problems -

    Translate everyday scenarios into linear equations and solve them using slope-intercept methods to build practical math confidence.

  5. Evaluate Equations Quickly -

    Develop speed and accuracy in answering slope intercept form questions, sharpening your ability to tackle algebra slope-intercept practice challenges.

Cheat Sheet

  1. Definition of Slope-Intercept Form -

    The slope-intercept form of a line, y = mx + b, clearly shows the slope (m) and y-intercept (b) so you can jump straight into graphing. Use the mnemonic "M = Move, B = Baseline" to remember how the line moves up or down and where it crosses the y-axis. Mastering this foundation will give you confidence on any slope intercept form quiz.

  2. Calculating Slope Between Two Points -

    To find slope in algebra slope-intercept practice, apply m = (y₂ - y₝)/(x₂ - x₝), a formula endorsed by Khan Academy and university math courses. For example, between (1,2) and (4,8), m = (8 - 2)/(4 - 1) = 2, which tells you the line rises 2 units for each 1 unit run. This reliable method is at the heart of every slope formula quiz.

  3. Graphing Using Slope and Intercept -

    Start your graph at the point (0, b) - the y-intercept - then use rise over run (m) to plot additional points, as recommended by MIT OpenCourseWare. For instance, y = - ½x + 4 means start at (0,4), then go down 1 and right 2. This simple two-step process makes any graphing slope intercept form quiz feel like a breeze.

  4. Understanding Slope Sign and Real-World Context -

    Positive slopes indicate increasing trends, negative slopes show decreases, zero slope means a flat line, and undefined slope is vertical - key insights in both math and real-world modeling. Imagine a rising ramp or a falling stock price to internalize how slope reflects change. Recognizing these patterns boosts your performance on slope intercept form questions involving context.

  5. Converting Standard Form to Slope-Intercept -

    Transform ax + by = c into y = ( - a/b)x + (c/b) to reveal m and b, a technique widely taught on Purplemath and in college algebra classes. For example, 3x + 2y = 6 becomes y = - (3/2)x + 3, instantly showing slope - 1.5 and intercept 3 for smoother problem-solving on any algebra slope-intercept practice session.

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