Linear Equations in Two Variables
The same line can be written as Ax + By = C (standard form) or y = mx + b (slope-intercept form) — same graph, two different ways to read it off.
Equations are often given in standard form, Ax + By = C. Rather than graphing from slope and y-intercept, it’s often faster to plot two points: the x-intercept (where the line crosses the x-axis, so y = 0) and the y-intercept (where it crosses the y-axis, so x = 0).
To find the x-intercept, set y = 0 and solve for x. To find the y-intercept, set x = 0 and solve for y. Once you have both points, you can draw the whole line — or check whether a given point lies on it by substituting and confirming both sides match.
The SAT frequently asks for an intercept directly, or gives you one and asks you to find a missing coefficient — both are just a matter of setting the right variable to zero. You’ll also see this topic tested through a table of values (find the slope from how much y changes per step in x), and through parallel and perpendicular lines: parallel lines share the same slope, while perpendicular lines have slopes that are negative reciprocals of each other (e.g., 2 and −1/2).