Compute slope and intercepts from an equation or graph. | Linear equations in two variables | SAT Math

Read slope and intercepts directly from slope-intercept form, standard form, or a graph.

核心知识

Slope is the rate of change $Δ 𝑦 Δ 𝑥$ . The y-intercept is where $𝑥 = 0$ ; the x-intercept is where $𝑦 = 0$ . Both can be read directly from the right equation form.

深入理解

If the equation is already in slope-intercept form $𝑦 = 𝑚 𝑥 + 𝑏$ , the slope is $𝑚$ and the y-intercept is $𝑏$ . If it's in standard form $𝐴 𝑥 + 𝐵 𝑦 = 𝐶$ , the slope is $- 𝐴 𝐵$ , the y-intercept is $𝐶 𝐵$ , and the x-intercept is $𝐶 𝐴$ .

From a graph, slope is rise over run between any two clear points. The y-intercept is where the line crosses the y-axis, and the x-intercept is where it crosses the x-axis.

A negative slope means the line falls from left to right. If you compute a positive slope but the line clearly goes downward, recheck your subtraction order.

分步讲解

For slope: rearrange to slope-intercept form and read $𝑚$ , or use $- 𝐴 𝐵$ from standard form.
For y-intercept: set $𝑥 = 0$ and solve for $𝑦$ .
For x-intercept: set $𝑦 = 0$ and solve for $𝑥$ .
From a graph: pick two lattice points and compute $r i s e r u n$ .

常见误解

Reading the coefficient of x as the slope in standard form — in $3 𝑥 + 5 𝑦 = 15$ , the slope is $- 35$ , not $3$ .
Confusing x-intercept and y-intercept — the y-intercept is a y-value (set $𝑥 = 0$ ), not an x-value.
Assuming a line with a large y-intercept has a steep slope — intercept and slope are independent.

题目

示例解析

What is the slope of the line $6 𝑥 + 3 𝑦 = 18$ ?

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