SAT Math: Write an equation given a point and slope
24+ practice questions in Praczo
The concept, explained
- 1
Point-slope form: y - y1 = m(x - x1), where m is the slope and (x1, y1) is any point on the line.
- 2
To plug in, subtract the point’s coordinates inside the parentheses — "y - y1" and "x - x1" — so signs flip on negative coordinates.
- 3
If the SAT answer choices are in slope-intercept form, distribute m(x - x1) and solve for y to convert.
- 4
If two points are given, first find the slope m = (y2 - y1)/(x2 - x1), then use either point in point-slope form.
- 5
Point-slope form makes it easy to write parallel/perpendicular lines: keep the given point and swap in the new slope.
- ✗ Forgetting to flip the sign when the point has a negative coordinate: for point (-3, 4), the form is y - 4 = m(x - (-3)) = m(x + 3).
- ✗ Using (x + x1) instead of (x - x1) in the formula.
- ✗ Mixing up which number is the slope and which is the y-coordinate of the point.
SAT-style practice
Which equation represents the line with slope 2 that passes through the point (-3, 5)?
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