➕ Algebra 1 · Linear Functions

Graphing Linear Equations practice questions

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Answer key with explanations

1. Which point is on the graph of y = 5x − 1?

   Answer: (2, 9). Substitute x = 2: y = 5(2) − 1 = 9, so (2, 9) is on the line. The point (9, 2) has its coordinates swapped. The point (2, 11) adds 1 instead of subtracting, and (2, 10) forgets the −1.

2. At which point does the graph of y = 6 − 4x cross the y-axis?

   Answer: (0, 6). Set x = 0: y = 6 − 4(0) = 6, so the graph crosses the y-axis at (0, 6). The y-intercept is 6. Written as y = −4x + 6, the number added by itself is b = 6, and −4 is the slope.

3. At which point does the line 2x − 5y = 20 cross the x-axis?

   Answer: (10, 0). A point on the x-axis has y = 0. Then 2x − 5(0) = 20, so 2x = 20 and x = 10. The line crosses the x-axis at (10, 0), so the x-intercept is 10. The point (0, −4) is where the line crosses the y-axis: setting x = 0 gives −5y = 20, so y = −4.

4. A line has y-intercept 2 and slope −3/4. Which point is also on the line?

   Answer: (4, −1). Start at (0, 2), where the line crosses the y-axis. A slope of −3/4 means a rise of −3 and a run of 4: go down 3 and right 4 to reach (4, −1). Check: −(3/4)(4) + 2 = −3 + 2 = −1. The point (4, 5) goes up instead of down, (−4, −1) goes down 3 but left 4, which is a slope of +3/4, and (3, −2) mixes up the rise and the run.

5. Which equation has a vertical line through (−6, 0) as its graph?

   Answer: x = −6. A vertical line has the same x-coordinate at every point. This line passes through (−6, 0), so its equation is x = −6. The equation y = −6 is a horizontal line through (0, −6), x = 6 is a vertical line on the other side of the y-axis, and y = −6x is a slanted line through the origin.

6. A table of values for a line shows x = 0, 1, 2, 3 and y = 5, 8, 11, 14. Which equation matches?

   Answer: y = 3x + 5. When x = 0, y = 5, so the y-intercept is 5 and b = 5. Each time x goes up by 1, y goes up by 3, so the slope is 3. The equation is y = 3x + 5. Check x = 3: 3(3) + 5 = 14.

7. A kiddie pool already holds 40 gallons, and a hose adds 6 gallons per minute. The equation y = 6x + 40 gives the gallons y after x minutes. Which statement about its graph is true?

   Answer: The graph crosses the y-axis at (0, 40): the 40 gallons already in the pool at the start.. Set x = 0: y = 6(0) + 40 = 40, so the y-intercept is 40 and the graph crosses the y-axis at (0, 40): the starting amount. The point (40, 0) is not on the graph, since at x = 40 the pool would hold 280 gallons. The graph misses the origin because the pool does not start empty. And at x = 6, y = 6(6) + 40 = 76, not 40.

8. Which equation has x-intercept 4 and y-intercept −6?

   Answer: 3x − 2y = 12. An x-intercept of 4 means the line passes through (4, 0), and a y-intercept of −6 means it passes through (0, −6). Test both points in each equation. For 3x − 2y = 12: 3(4) − 2(0) = 12 and 3(0) − 2(−6) = 12. Both work. Each of the others fails at least one: 3x + 2y = 12 has y-intercept 6, 2x − 3y = 12 has x-intercept 6, and −3x + 2y = 12 has x-intercept −4.

9. Dana graphed y = −3x + 2 by plotting (0, 2) and then going up 3 and right 1 to (1, 5). What went wrong?

   Answer: She ignored the negative sign. A slope of −3 means down 3 for each 1 to the right, which reaches (1, −1).. The slope is −3, which is −3/1: down 3 and right 1 from (0, 2), reaching (1, −1). Check: −3(1) + 2 = −1. Dana’s point (1, 5) would need a slope of +3.