Digital SAT · Math · Algebra. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
A linear equation in two variables, such as 3x + 2y = 12, has many solutions. Each solution is a pair (x, y), and together the pairs form a straight line in the xy-plane.
Two forms are used most. Slope-intercept form, y = mx + b, shows the slope and the y-intercept at once. Standard form, Ax + By = C, is common in contexts where two kinds of item share one total, for example price × number + price × number = total cost.
To find an intercept, set the other variable to 0. To compare lines, compare slopes: parallel lines have equal slopes, and the slopes of perpendicular lines multiply to −1.
Reading the slope straight from standard form. In 3x − 2y = 5 the slope is not 3; rearrange to y = (3/2)x − 5/2 first, which gives slope 3/2.
Answer: y = (3/2)x + 2
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