Point-slope form
SAT glossary · Math
Definition
y-y_1 = m(x-x_1); the form that exists exactly for writing a line from a point and a rate. The dominant error on that item type is y = mx + y_1 — reading the given point's y-value as the intercept — which the verification step (plug the point back in) catches free.
Point-slope form in plain English
Point-slope form, y-y_1=m(x-x_1), exists for one specific job: writing the equation of a line when you know just ONE point on it, (x_1,y_1), and its slope m. The most common mistake with this form is accidentally writing y=mx+y_1 instead — mistakenly treating the given point's y-value as if it were the line's y-INTERCEPT (the value where x=0), which it usually isn't. The best defense against this mistake is simple: once you've written your final equation, plug your original point back in and confirm it actually makes the equation true — if it doesn't check out, you made this exact substitution error.
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