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Quizzes > High School Quizzes > Mathematics

8th Grade Math Worksheets: Linear Equations Practice Quiz

Master Algebra 1, Slope, and Function Skills Today

Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Colorful paper art promoting Slope Line Quest trivia for high school math students.

What is the slope of a horizontal line?
0
Undefined
1
No slope
A horizontal line does not have any rise, which means its slope is 0. There is no change in the y-value as x increases.
What is the slope of a vertical line?
Undefined
0
1
Infinite
A vertical line has an undefined slope because the change in x is zero, making the slope formula result in division by zero. Therefore, the slope cannot be determined using the standard formula.
Which equation is already in slope-intercept form?
y = 3x + 2
3x + y = 2
y - 3x = 2
x = 3y + 2
The slope-intercept form is written as y = mx + b, where m is the slope and b is the y-intercept. The equation y = 3x + 2 clearly shows both the slope and y-intercept in the proper format.
Identify the slope from the equation y = -4x + 7.
-4
7
-7
4
In the equation y = mx + b, the coefficient of x represents the slope. Here, the coefficient is -4, which indicates the line falls 4 units in y for every 1 unit increase in x.
What is the y-intercept of the line represented by y = 2x - 5?
-5
2
5
0
In the slope-intercept form y = mx + b, the term b represents the y-intercept. For the equation y = 2x - 5, the y-intercept is -5.
Find the slope of the line passing through points (2, 3) and (6, 11).
2
4
8
1
The slope is calculated using the formula (y₂ - y₝) / (x₂ - x₝). Substituting the given points results in (11 - 3) / (6 - 2) = 8/4 = 2.
Determine the equation of the line with slope 3 and y-intercept -2.
y = 3x - 2
y = 3x + 2
y = -3x - 2
y = -2x + 3
The slope-intercept form is given as y = mx + b. With m = 3 and b = -2, the correct equation is y = 3x - 2.
Which of the following is parallel to the line y = 0.5x + 4?
y = 0.5x - 3
y = -0.5x + 4
y = 2x + 1
y = -2x - 1
Parallel lines have the same slope. Since the given line has a slope of 0.5, the line y = 0.5x - 3, which also has a slope of 0.5, is parallel.
Which of the following lines is perpendicular to the line with slope 2?
y = (-1/2)x + 3
y = (1/2)x - 1
y = 2x + 1
y = -2x - 3
For two lines to be perpendicular, the product of their slopes must be -1, meaning the perpendicular slope is the negative reciprocal. Here, the negative reciprocal of 2 is -1/2.
What is the slope of the line given by 4y = 8x - 12?
2
-2
4
-4
By dividing both sides of the equation by 4, we obtain y = 2x - 3. The coefficient of x in this form is the slope, which is 2.
What are the slope and y-intercept of the line represented by y = -3x + 9?
Slope: -3, y-intercept: 9
Slope: 3, y-intercept: 9
Slope: -3, y-intercept: -9
Slope: 9, y-intercept: -3
In the equation y = mx + b, m is the slope and b is the y-intercept. Thus, y = -3x + 9 indicates a slope of -3 and a y-intercept of 9.
Write the equation of the line that passes through the point (1, 2) with a slope of 5.
y = 5x - 3
y = 5x + 3
y = x + 5
y = 3x - 5
Using the point-slope form, y - y₝ = m(x - x₝), and substituting m = 5 and the point (1, 2) gives y - 2 = 5(x - 1). Simplifying results in y = 5x - 3.
If two lines are parallel, which of the following must be true about their slopes?
Their slopes are equal
Their slopes are opposite reciprocals
Their slopes multiply to -1
One slope is the negative of the other
Parallel lines have identical slopes, ensuring that they never intersect. This condition is fundamental for two lines to be parallel.
What happens to the graph of a line if the y-intercept is increased by 4 units, keeping the slope unchanged?
It shifts upward by 4 units
It shifts downward by 4 units
It rotates clockwise
It becomes steeper
Changing the y-intercept moves the line vertically without affecting its slope. Increasing the intercept by 4 units shifts the entire line upward by that amount.
Find the x-intercept of the line given by 3x + 2y = 12.
4
12
3
6
To find the x-intercept, set y = 0 in the equation 3x + 2y = 12. This simplifies to 3x = 12, giving x = 4.
Given two points on a line, (a, 2) and (4, b), and knowing the slope is 3, what is the relationship between a and b?
b = 14 - 3a
b = 3a - 14
b = a + 3
b = 3a + 14
Using the slope formula (b - 2) / (4 - a) = 3, we multiply both sides by (4 - a) to get b - 2 = 12 - 3a. Adding 2 to both sides yields b = 14 - 3a, which is the required relationship.
Solve for m in terms of a line passing through (m, 2) and (4, 8) when the slope is 3.
2
4
-2
6
Applying the slope formula (8 - 2) / (4 - m) = 3 gives 6/(4 - m) = 3. Solving 6 = 3(4 - m) leads to m = 2.
Determine the equation of the line that is perpendicular to y = (1/2)x - 3 and passes through the point (4, 1).
y = -2x + 9
y = 2x - 9
y = -2x - 9
y = 2x + 9
A line perpendicular to another has a slope that is the negative reciprocal of the original slope. Since the original slope is 1/2, the perpendicular slope is -2, and using the point-slope formula with (4, 1) leads to y = -2x + 9.
If a line's equation is given by 7y - 14x = 21, what is its slope?
2
-2
7
21
Rearranging the equation to slope-intercept form by isolating y gives 7y = 14x + 21, or y = 2x + 3. The slope is the coefficient of x, which is 2.
Find the intersection point of the lines y = 2x + 1 and y = -x + 7.
(2, 5)
(2, -5)
(-2, 5)
(-2, -5)
Setting 2x + 1 equal to -x + 7 allows us to solve for x: 3x = 6, so x = 2. Substituting x = 2 back into either equation gives y = 5, resulting in the intersection point (2, 5).
0
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Study Outcomes

  1. Define and calculate slopes from given points.
  2. Interpret and apply different forms of linear equations.
  3. Analyze the relationship between slopes of parallel and perpendicular lines.
  4. Graph linear equations and identify key characteristics of the line.
  5. Solve real-world problems using slope and linear equation concepts.

8th Grade Linear Equations Cheat Sheet

  1. Understand the slope-intercept form - The equation y = mx + b shows how slope (m) and y-intercept (b) define a line, making it super simple to sketch and interpret linear relationships. Once you've got this down, you can tweak m and b to see instant changes on your graph. GeeksforGeeks Practice Problems
  2. Calculate the slope between two points - Use m = (y₂ - y₝) / (x₂ - x₝) to figure out how steep your line is and which way it's tilting. This formula turns any two points into a clear direction and rate of change. Wyzant Slope Tips
  3. Convert standard form to slope-intercept form - Rearrange Ax + By = C to isolate y, revealing y = mx + b in all its glory. Mastering this lets you jump straight into graphing without missing a beat. GeeksforGeeks Conversion Guide
  4. Use the point-slope form - When you know a point (x₝, y₝) and the slope m, plug into y - y₝ = m(x - x₝) for an instant line equation. It's your shortcut to precise graphing without extra algebraic gymnastics. GeeksforGeeks Point-Slope Practice
  5. Recognize horizontal and vertical lines - Horizontal lines (slope = 0) look like y = c, while vertical lines (undefined slope) are x = a. Knowing this helps you spot and draw these special cases in a snap. GeeksforGeeks Special Lines
  6. Practice solving linear equations - Isolate variables, combine like terms, and use inverse operations to crack any linear equation. These steps become second nature with a bit of consistent practice. Lamar University SolveLinearEqns
  7. Graph lines using intercept and slope - Start by plotting the y‑intercept, then use the slope "rise over run" to place a second point. Connect the dots and watch your line come to life. MathBits Notebook Graph Practice
  8. Find an equation from two points - First calculate the slope, then plug one of the points into the point-slope formula to derive y = mx + b. This two-step method is foolproof once you get the hang of it. MathBits Notebook Equation Creation
  9. Identify parallel and perpendicular lines - Parallel lines share the same slope, and perpendicular lines have slopes that are negative reciprocals. Spotting these relationships is key in geometry and graph analysis. GeeksforGeeks Parallel vs Perpendicular
  10. Tackle real-world linear problems - Translate situations into linear equations, then interpret slope and intercept within context to draw meaningful conclusions. These skills turn abstract math into practical solutions. Pearson College Algebra Prep
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