Perpendicular slopes are negative reciprocals: turn the slope over and change its sign. These free printable worksheets give a point and a line in standard form, such as x + 4y = 8, and ask for the perpendicular line through the point as y = mx + b.
If they get stuck
The answer key prints on a separate page.
There are three steps, and the key writes each one. Through (−1, 2) perpendicular to x + 4y = 8: rearrange to 4y = −x + 8 and y = −¼x + 2, so the given slope is −¼; turn it over and change the sign, so m = 4; then b = 2 − (4)(−1) = 6, and the line is y = 4x + 6. Most errors are in the middle step. A student who turns the slope over but keeps its sign writes a line that is not perpendicular, and nothing in the later arithmetic shows it.
The given line is in standard form on purpose. A perpendicular slope is a reciprocal, so one of the two slopes has to be a fraction; putting the fraction in the given line, where it is read rather than written, keeps every answer a whole slope from −4 to 4 with a whole intercept. Reading the slope out of x − 2y = 4 means rearranging it to y = ½x − 2 first, and that rearrangement is half the practice.