8.2 SAT Math - Slope-Intercept Formula

Slope-Intercept Formula is the most common slope formula you'll use:

y = mx + b

where m is your slope and b is your y-intercept.  An intercept is the point at which the line crosses the axis.  To find your intercepts quickly, plug in 0 for the opposite variable.  So if you want your y­-intercept, plug in 0 for x.  If you're looking for your x­-intercept, plug in 0 for y.
If you know other formulas involving slope, like point-slope formula, feel free to use them, but it's usually easiest to just stick with Slope-Intercept and solve from there.

For example, if you're given only two points, start by finding your slope using , plug that answer in for m, and then solve for b.  If you're given the slope, you're already halfway there, and all you need to do is find b to find the equation of the line.

If you're given a graph, the slope is the distance up over the distance over.  Start from any clear point on the line, count up the number of spaces you need to get to the next point, and count over the number of spaces you need to get to the next point.  That's your slope.

Parallel lines have equal slopes.  Perpendicular lines have negative reciprocal slopes, that is, write the slope of your line as a fraction, flip it over, and change the sign to find the slope of the perpendicular line.  So if your original slope was -3, the slope of the perpendicular line would be positive 1/3.

-SAT Math Tip: Watch your slope whenever you're answering a question in which you were supposed to find the equation of a line!  The wrong answer choices often look very very tempting, but the slope is wrong, either by being upside down, or the wrong sign, or just plain "off."  Any equation you find should match yours exactly.  If you found an equation in slope-intercept form and the answers are in Standard Form, don't guess.  Manipulate your equation into the proper format before selecting an answer, and then see which answer choice matches.  For example, if you found the equation to be y = (1/4)x + 2 and all the answers are in the form Ax + By = C, you'll need to make your equation look like that.  Get rid of the fraction by multiplying the whole equation by the value in the denominator, and move all your variables to one side.  From there, you may need to multiply through by -1 to get your x to be positive:

Always do that work before you go to the answer choices.  Otherwise, you are very likely to fall for SAT tricks, selecting an answer with the wrong positive/negatives, or one number off.