➕ Algebra 1 · Linear Functions
Slope-Intercept Form: true or false
Decide fast, then read the reason. Wrong answers are the best teachers, so every statement explains itself.
All statements and answers
In y = mx + b, the letter b is the slope.
✗ False. m is the slope. b is the y-intercept.
The line y = 3x − 5 crosses the y-axis at (0, −5).
✓ True. At x = 0, y = 3(0) − 5 = −5.
The slope of y = 6 − 2x is 6.
✗ False. Rewrite it as y = −2x + 6. The slope is −2, and 6 is the y-intercept.
A vertical line can be written in slope-intercept form by choosing m = 0.
✗ False. m = 0 gives a horizontal line. A vertical line has an undefined slope, so it has no m. Its equation is x = a.
The line y = 8 has slope 0.
✓ True. y = 0x + 8 is a horizontal line: the rise is 0 for any run.
A line with slope 2 through (1, 7) has the equation y = 2x + 7.
✗ False. The 7 is a y-value at x = 1, not at x = 0. Substitute: 7 = 2(1) + b, so b = 5 and the equation is y = 2x + 5.
The y-intercept is the value of y when x = 0.
✓ True. The line meets the y-axis where x = 0, and the y-value at that point is the y-intercept.
In a story where x starts at 0, the slope is the rate of change and the y-intercept is the starting value.
✓ True. The slope tells how much y changes per 1 unit of x, and the y-intercept is the value of y when x = 0, which is the start of the story here.
The line through (0, 1) and (2, 11) has the equation y = 5x + 1.
✓ True. The slope is (11 − 1) ÷ (2 − 0) = 5, and the point (0, 1) gives b = 1. Check the other point: 5(2) + 1 = 11.
A line with slope −2/3 goes down 2 units for every 3 units to the right.
✓ True. −2/3 means a rise of −2 and a run of 3, so the line goes down 2 as it goes right 3.
5x + y = 9 is not in slope-intercept form, but it can be rewritten as y = −5x + 9.
✓ True. Subtract 5x from both sides to get y = −5x + 9, which has the form y = mx + b.
Two lines with the same y-intercept must have the same slope.
✗ False. y = x + 3 and y = −2x + 3 both cross the y-axis at (0, 3), but their slopes are 1 and −2.