Linear Functions • Topic 4 of 7

Equation of Line

A line is determined by its slope and a point, or by two points. The usual recipe: find the slope, then use it with a known point to write the equation, most often in slope-intercept form y = mx + b. If you know the slope m and the y-intercept b, you can write the equation directly. From two points, compute the slope first, then solve for b using one of the points. Producing the correct equation of a line from given information is among the most common SAT algebra tasks.

✅ Solved examples

1. Write the equation of the line with slope 2 and y-intercept 5.
y = mx + b = 2x + 5.
2. A line has slope 3 and passes through (0, −4). Equation?
The y-intercept is −4, so y = 3x − 4.
3. A line has slope 2 and passes through (1, 5). Find b.
5 = 2(1) + b → b = 3, so y = 2x + 3.
4. Write the equation through (0, 0) with slope −1.
y-intercept 0, so y = −x.

✏️ Practice — try these, take hints as needed

1. Write the line with slope 4 and y-intercept −1.
Use y = mx + b.
m = 4, b = −1.
—
y = 4x − 1.
2. A line has slope 5 and passes through (0, 2). Equation?
(0, 2) gives the y-intercept.
b = 2.
y = 5x + b.
y = 5x + 2.
3. A line has slope 3 and passes through (2, 10). Find b.
10 = 3(2) + b.
10 = 6 + b.
Solve for b.
b = 4 (y = 3x + 4).
4. Write the line through (0, −3) with slope 1.
y-intercept −3.
m = 1.
—
y = x − 3.
5. A line has slope −2 and passes through (1, 1). Find b.
1 = −2(1) + b.
1 = −2 + b.
Solve.
b = 3 (y = −2x + 3).

📝 Topic test — 8 questions

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