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Quizzes > High School Quizzes > Mathematics

Equation Practice Quiz: Slope and Y-Intercept

Master writing linear equations with confidence

Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Paper art promoting The Slope-Intercept Showdown quiz for high school algebra students.

Easy
Write the equation of a line with a slope of 3 and a y-intercept of -2.
y = -2x + 3
y = 2x - 3
y = -3x + 2
y = 3x - 2
In the slope-intercept form y = mx + b, m is the slope and b is the y-intercept. Substituting m = 3 and b = -2 gives y = 3x - 2.
In the equation y = -4x + 7, what is the y-intercept?
4
-4
-7
7
The y-intercept in the equation y = mx + b is represented by b. Here, b equals 7.
Which form of a linear equation is known as the slope-intercept form?
(x - h)² + (y - k)² = r²
y - y₝ = m(x - x₝)
y = mx + b
ax + by = c
The slope-intercept form of a line is written as y = mx + b, where m represents the slope and b represents the y-intercept. The other forms represent standard form, point-slope form, and the equation of a circle.
What is the slope of the line represented by y = 5x + 3?
3
5
-5
-3
In the equation y = 5x + 3, the coefficient of x, which is 5, represents the slope of the line. Therefore, the slope is 5.
Find the equation of a line with a y-intercept of 0 and a slope of -1.
y = -x + 1
y = x - 1
y = -x
y = x
A slope of -1 with a y-intercept of 0 means the line passes through the origin and declines at a 45-degree angle. Thus, the equation is y = -x.
Medium
Write the equation of a line with a slope of -2 and a y-intercept of 5.
y = 2x - 5
y = -2x - 5
y = 2x + 5
y = -2x + 5
Inserting the given slope (m = -2) and y-intercept (b = 5) into the slope-intercept form y = mx + b results in y = -2x + 5. This directly follows the definition of the slope-intercept form.
For the line given by y = (1/2)x - 3, what is the value of y when x = 8?
1
5
3
-1
Substitute x = 8 into the equation: y = (1/2)*8 - 3 = 4 - 3 = 1. Hence, when x is 8, y equals 1.
Convert the equation 4y = 8x - 12 to slope-intercept form.
y = 2x + 3
y = 8x - 12
y = 4x - 12
y = 2x - 3
Dividing both sides of the equation 4y = 8x - 12 by 4 yields y = 2x - 3. This is the slope-intercept form, with a slope of 2 and a y-intercept of -3.
A line has a slope of 3 and passes through the point (0, 2). Which equation represents this line?
y = 2x + 3
y = 3x - 2
y = 2x - 3
y = 3x + 2
Since the line passes through (0, 2), the y-intercept is 2. With a given slope of 3, the equation becomes y = 3x + 2.
Find the slope-intercept form of the line passing through the points (1, 4) and (3, 8).
y = 2x + 4
y = 4x + 2
y = 2x + 2
y = 4x - 2
The slope between the points is (8 - 4) / (3 - 1) = 2. Using point (1, 4), substitute into y = mx + b: 4 = 2(1) + b gives b = 2. Thus, the equation is y = 2x + 2.
Determine the equation of a line parallel to y = -x + 1 that goes through the point (2, -3).
y = -x - 1
y = x - 1
y = x + 5
y = -x + 5
Parallel lines share the same slope. Since y = -x + 1 has a slope of -1, the line through (2, -3) must also have slope -1. Substituting into y = -x + b with (2, -3) gives b = -1, so the equation is y = -x - 1.
Find the x-intercept of the line given by y = 3x - 9.
-9
-3
9
3
To find the x-intercept, set y = 0. Solving 0 = 3x - 9 gives 3x = 9, so x = 3. The x-intercept is therefore 3.
What effect does increasing the y-intercept in the slope-intercept form have on the graph of a line?
It shifts the line upward without changing its slope.
It makes the line steeper.
It shifts the line downward.
It rotates the line.
The y-intercept determines where the line crosses the y-axis. Increasing it moves the entire line upward while leaving the slope, or steepness, unchanged.
What is the slope-intercept form of a line given that the slope is 0 and the y-intercept is 4?
y = -4
y = 4x
y = 0
y = 4
When the slope is 0, the line is horizontal and the equation simplifies to y equal to the y-intercept. Thus, with a y-intercept of 4, the equation is y = 4.
If a line's equation is y = mx + 8 and it passes through the point (2, 14), what is the value of m?
3
2
4
6
Substitute the point (2, 14) into the equation: 14 = 2m + 8. Solving 14 - 8 = 2m yields m = 3. Therefore, the slope m is 3.
Hard
For the equation 2(2y - 1) = 4x + 10, rewrite it in slope-intercept form and identify the slope and y-intercept.
Slope = 1, y-intercept = -3
Slope = 1, y-intercept = 3
Slope = 2, y-intercept = 3
Slope = 3, y-intercept = 1
Expanding the given equation: 2(2y - 1) becomes 4y - 2, so the equation is 4y - 2 = 4x + 10. Adding 2 to both sides gives 4y = 4x + 12; dividing by 4 yields y = x + 3. Thus, the slope is 1 and the y-intercept is 3.
Two lines are defined by y = 2x + 1 and y = mx - 3. If these lines are perpendicular, what is the value of m?
-1/2
-2
2
1/2
For two lines to be perpendicular, the product of their slopes must be -1. Given the first line's slope is 2, the second line must have a slope of -1/2 to satisfy 2 - (-1/2) = -1.
A line has the equation y = kx + 4 and passes through the point (3, 10). What is the value of k?
4
-2
3
2
Substitute the point (3, 10) into the equation: 10 = 3k + 4. Solving 10 - 4 = 3k gives k = 2. Therefore, the correct value of k is 2.
What is the equation of a line that is parallel to 3y - 6x = 12 and passes through the point (0, -2)?
y = 2x + 2
y = -2x - 2
y = 2x - 2
y = -2x + 2
First, convert 3y - 6x = 12 to slope-intercept form: 3y = 6x + 12 and then y = 2x + 4. The slope here is 2. A line parallel to this must also have a slope of 2; using the point (0, -2) gives the equation y = 2x - 2.
Solve for the unknown slope m in the equation y = mx - 1, given that the line passes through (-2, 3).
-2
-1
2
1
Substitute the point (-2, 3) into the equation: 3 = m(-2) - 1. This simplifies to 3 + 1 = -2m, so 4 = -2m, and thus m = -2. The correct value of m is -2.
0
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Study Outcomes

  1. Identify the slope and y-intercept in linear equations.
  2. Construct the equation of a line given its slope and y-intercept.
  3. Analyze how changes in slope and y-intercept affect the line's graph.
  4. Apply the slope-intercept form to solve related algebra problems.

Write Equation Worksheet: Slope & Y-Intercept Cheat Sheet

  1. Understand slope-intercept form - Kick things off by mastering y = mx + b, where m tells you how steep the line is and b shows where it crosses the y-axis. It's the secret sauce for graphing linear equations in a snap! SplashLearn's Slope-Intercept Guide
  2. Identify slope and y-intercept - Spot m and b like a math detective! For example, in y = 2x + 3, m = 2 means the line rises two units for every one unit it goes right, and b = 3 is where your line hits the y-axis first. GeeksforGeeks Slope-Intercept Basics
  3. Write equations from slope and intercept - Turn numbers into equations like a boss: if m = - 4 and b = 5, simply plug in to get y = - 4x + 5. Repeating this builds muscle memory and confidence! Practice Writing Equations on MathPlanet
  4. Convert standard form to slope-intercept - Flip Ax + By = C into y = mx + b by solving for y. For instance, 2x - 3y = 6 becomes y = (2/3)x - 2 so you can graph it at a glance! GFG Practice: Standard to Slope-Intercept
  5. Find slope from two points - Use m = (y₂ - y₝)/(x₂ - x₝) to figure out steepness between any two points. For (2, 4) and (4, 8), that's (8 - 4)/(4 - 2) = 2, so the line shoots up two units every run of one! GFG Guide: Finding Slope Between Two Points
  6. Graph a line using slope and y-intercept - Start at the y-intercept and then use rise/run to plot your next point - no rocket science needed. Connect the dots, and voila, your line is ready for showtime! Graphing Tips on MathPlanet
  7. Write equations from a graph - Read off the y-intercept, count your rise over run on the grid, then pack them into y = mx + b. If the line crosses at 1 and slopes down 2 for every 3 right, you get y = ( - 2/3)x + 1. MathPlanet's Graph-to-Equation Drill
  8. Understand horizontal and vertical lines - Dream big with zero slope and infinite steepness: horizontal lines look like y = b (they never tilt), while vertical lines are x = a (they go straight up!). Recognizing these special cases is like having cheat codes for graphing. Special Lines with GFG
  9. Convert point-slope to slope-intercept - Start with y - y₝ = m(x - x₝) and simply distribute and solve for y. For instance, y - 2 = 3(x - 1) transforms into y = 3x - 1 for a quick graph-friendly form. GFG Point-Slope to Slope-Intercept
  10. Apply to real-world problems - Model pizza delivery fees or taxi fares using y = mx + b, where b is your base fee and m is cost per mile or item. Applying slope-intercept form to everyday scenarios makes math feel like magic! GFG Real-World Slope-Intercept Problems
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