Read the Line in Its Own Places

You'll learnto read a line's slope and y-intercept from y = mx + b without swapping them.

In y = mx + b, two numbers live in two places and describe two different things: m is the steepness, b is where the line crosses. Swap them and every reading goes wrong. Watch slope built as rise over run, the two moves a perpendicular slope actually needs, and why f(3) is a lookup — never f times 3.

8 STEPS · 6 QUICK CHECKS · m is the slope · b is the intercept · f(3) is a lookup · v3

y = mx + b

Before you start

What you're looking at

A coordinate plane with the line y = −4x + 3, marked where it crosses the y-axis at (0, 3), beside a reading card.

The question

Which number in y = −4x + 3 is the slope, and which is the y-intercept?

Watch for

The line crosses the y-axis at 3 and falls steeply going right; notice the negative slope tilts it downward.

What the symbols mean

In y = mx + b, m is the slope — the coefficient on x — and b is the y-intercept, the lone constant.

Keep separate

The y-intercept is the height where x = 0. Where a line crosses the x-axis is a third thing entirely — that's where y = 0.

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