Linear Functions • Topic 6 of 7

Slope-Intercept Form

Slope-intercept form, y = mx + b, is the most useful form for graphing and reading a line: m is the slope and b is the y-intercept (where the line crosses the y-axis). To graph, plot (0, b) then use the slope as rise/run to find more points. To find where a line meets the x-axis, set y = 0 and solve. Rewriting other forms into y = mx + b makes the slope and intercept obvious, which is why the SAT so often wants answers in this form or asks you to identify m or b from it.

✅ Solved examples

1. For y = 4x − 3, name the slope and y-intercept.
Slope m = 4 and y-intercept b = −3.
2. Rewrite 2x + y = 5 in slope-intercept form.
Subtract 2x: y = −2x + 5.
3. Where does y = 2x − 6 cross the x-axis?
Set y = 0: 0 = 2x − 6 → x = 3.
4. What is the y-intercept of y = −5x + 7?
b = 7, so the line crosses the y-axis at (0, 7).

✏️ Practice — try these, take hints as needed

1. For y = −3x + 8, name the slope and y-intercept.
m is the x-coefficient.
b is the constant.
—
m = −3, b = 8.
2. Rewrite 3x + y = 9 in slope-intercept form.
Subtract 3x.
y = −3x + 9.
—
y = −3x + 9.
3. Where does y = 3x − 12 cross the x-axis?
Set y = 0.
0 = 3x − 12.
Solve for x.
x = 4.
4. What is the y-intercept of y = 2x − 9?
b is the constant term.
Read it off.
—
−9.
5. Rewrite 4x − 2y = 8 in slope-intercept form.
−2y = −4x + 8.
Divide by −2.
—
y = 2x − 4.

📝 Topic test — 8 questions

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