➕ Algebra 1 · Linear Functions

Slope-Intercept Form practice questions

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Answer key with explanations

1. What are the slope and y-intercept of y = −6x + 11?

   Answer: m = −6, b = 11. The number multiplying x is the slope: m = −6. The constant added on its own is the y-intercept: b = 11. The line crosses the y-axis at (0, 11).

2. Where does the line y = 2x − 9 cross the y-axis?

   Answer: (0, −9). Points on the y-axis have x = 0. Then y = 2(0) − 9 = −9, so the line crosses at (0, −9). The point (9/2, 0) is where the line crosses the x-axis, not the y-axis.

3. A line crosses the y-axis at (0, 4) and rises 5 units for every 2 units to the right. Which equation is it?

   Answer: y = (5/2)x + 4. The y-intercept is b = 4. The slope is rise ÷ run = 5/2. So y = (5/2)x + 4. Check: from (0, 4), going right 2 and up 5 reaches (2, 9), and (5/2)(2) + 4 = 9.

4. A line has slope 3 and passes through (2, 11). What is its equation?

   Answer: y = 3x + 5. Put m = 3 into y = mx + b and substitute the point: 11 = 3(2) + b. That gives 11 = 6 + b, so b = 5 and y = 3x + 5. The y-value 11 is not b, because the point has x = 2, not x = 0.

5. Which equation describes the line through (3, 4) and (5, −4)?

   Answer: y = −4x + 16. The slope is (−4 − 4) ÷ (5 − 3) = −8 ÷ 2 = −4. Substitute (3, 4): 4 = −4(3) + b, so 4 = −12 + b and b = 16. The equation is y = −4x + 16. Check (5, −4): −4(5) + 16 = −4.

6. A skate park membership costs 14 dollars per month, and each visit costs 3 dollars. Which equation gives the monthly cost C in dollars for v visits?

   Answer: C = 3v + 14. Each visit adds 3 dollars, so the slope is m = 3. With 0 visits you still pay 14 dollars, so b = 14. The equation is C = 3v + 14. For example, 5 visits cost 3(5) + 14 = 29 dollars. Only whole numbers of visits, v = 0, 1, 2, …, make sense, so only part of the line fits the story.

7. Which equation cannot be written in the form y = mx + b?

   Answer: x = 10. x = 10 is a vertical line. Its slope is undefined (the run is 0), so there is no number m for y = mx + b. The others can be written that way: y = 10 is y = 0x + 10, y = 10x is y = 10x + 0, and x + y = 10 is y = −x + 10.

8. A lunch card’s balance in dollars after w weeks is B = −8w + 50. Which statement is correct?

   Answer: The card started with 50 dollars, and the balance drops 8 dollars each week.. At w = 0 the balance is −8(0) + 50 = 50 dollars, so the y-intercept 50 is the starting balance. The slope −8 means the balance changes by −8 dollars each week, so it drops 8 dollars per week. The other choices swap the roles of 8 and 50 or get the direction wrong. The equation also stops fitting after w = 50 ÷ 8 = 6.25 weeks, when the balance would go below 0.

9. Rewrite x − 3y = 12 in slope-intercept form.

   Answer: y = (1/3)x − 4. Subtract x from both sides: −3y = −x + 12. Divide every term by −3: y = (1/3)x − 4. Check with x = 3: y = 1 − 4 = −3, and 3 − 3(−3) = 12.