Eighth grade brings linear equations and lines together. Students solve linear equations in one variable, including ones with variables on both sides, the distributive property and decimal coefficients, and decide whether an equation has one solution, no solution or infinitely many (Common Core 8.EE.C.7). They also connect proportional relationships to slope (8.EE.B.5) and explain why a line can be written as y = mx + b, where m is the slope and b is the y-intercept (8.EE.B.6).
This set mixes equation solving with slope from two points, reading m and b from an equation, a real-world cost problem and special cases with no solution or infinitely many. For equations, do the same thing to both sides and check your answer by substituting it back in. For slope, use rise over run: subtract the y-values, subtract the x-values in the same order, and divide. Type equation answers as a number or as x = 5. Every question is checked instantly with a full worked solution.
Choose an option or type your answer, then press Check. Capital letters and extra spaces do not matter in typed answers, and units are optional.
Answer: 5 (also accepted: x = 5, x=5)
Subtract 7 from both sides: 3x = 15. Divide both sides by 3: x = 5. Check: 3(5) + 7 = 22.
Answer: B) x = 9
Distribute: 2x - 8 = 10. Add 8 to both sides: 2x = 18. Divide by 2: x = 9. Check: 2(9 - 4) = 2(5) = 10.
Answer: 2
Slope = (11 - 3) / (6 - 2) = 8 / 4 = 2.
Answer: B) -3
In y = mx + b, m is the slope. Here m = -3, so the slope is -3. The 4 is the y-intercept.
Answer: 6 (also accepted: x = 6, x=6)
Subtract 2x from both sides: 3x - 4 = 14. Add 4: 3x = 18. Divide by 3: x = 6. Check: 5(6) - 4 = 26 and 2(6) + 14 = 26.
Answer: B) -5
In y = mx + b, b is the y-intercept. Here b = -5, so the line crosses the y-axis at (0, -5).
Answer: -2
Slope = (-4 - 4) / (3 - (-1)) = -8 / 4 = -2. The line goes down from left to right, so a negative slope makes sense.
Answer: B) y = 4x - 1
Put m = 4 and b = -1 into y = mx + b: y = 4x - 1.
Answer: 12 (also accepted: x = 12, x=12)
Subtract 3 from both sides: 0.5x = 6. Divide by 0.5 (or multiply by 2): x = 12.
Answer: C) Infinitely many
Distribute the right side: 2(x + 3) = 2x + 6. Both sides are identical, so every value of x works. There are infinitely many solutions.
Answer: 7 (also accepted: 7 months)
Write the equation 15m + 25 = 130. Subtract 25: 15m = 105. Divide by 15: m = 7 months.
Answer: B) None
Subtract 4x from both sides: 1 = -3. That is never true, so the equation has no solution. (The lines y = 4x + 1 and y = 4x - 3 are parallel.)
Answer: 20 (also accepted: x = 20, x=20)
Add 2 to both sides: x/4 = 5. Multiply both sides by 4: x = 20. Check: 20/4 - 2 = 3.
Answer: B) 5
The y-intercept is 2, so the equation is y = (1/2)x + 2. When x = 6, y = 3 + 2 = 5.
2(x - 4) is 2x - 8, not 2x - 4. Multiply every term inside the parentheses.
Slope is (y2 - y1) / (x2 - x1). Using y2 - y1 on top but x1 - x2 underneath flips the sign.
In y = -3x + 4 the slope is -3 (the number with x) and the y-intercept is 4.
If the variables cancel and you get a true statement such as 6 = 6, there are infinitely many solutions. A false statement such as 1 = -3 means no solution.
Turn linear equations into a printable, differentiated worksheet with an answer key, matched to grade 8.
Make a worksheet βBuild a test or quiz on this topic that students answer online and that marks itself, with a class summary for you.
Build a self-marking test βStep-by-step help, quizzes and test-style practice in a safe, parent-managed student portal.
Open the student portal βSubtract the y-coordinates and divide by the difference of the x-coordinates in the same order: slope = (y2 - y1) / (x2 - x1).
When both sides simplify to exactly the same expression, such as 2x + 6 = 2(x + 3), every value of x makes the equation true.