Linear Equations Cheat Sheet
| Standard Form | Slope Intercept Form | Point Slope Form | Slope Equation | |
| ax + by = c | y = mx + b | y - y1 = m(x - x1) | ||
| Slope = -a/b | Slope = m | Slope = m |
m = |
(y2 - y1) |
| (x2 - x1) | ||||
| When to Use: | ||||
| When given a slope and a point | When given a slope and a point | When given a point and a slope | When given two points and you need a slope | |
| How to Use: | ||||
| Using the slope, identify "a" and "b". Then plug in a, b x, and y. Solve for c. Rewrite the equation using only a,b and c, keep x and y as x and y. | Plug in the slope for "m" and the ordered pair for x and y. Solve for b. Rewrite the equation using values for m and b, keep x and y as x and y. | Plug the point coordinates in for "x1" and "y1" and the slope in for "m". Rearrange the equation into the desired form. | Follow equation | |
| When To Use: | ||||
| When you need to find the slope from an equation | When given a slope and a y-intercept | When given two points, and you need to find a line | ||
| How to Use: | ||||
| take the opposite of the x coefficient over the y coefficient to get the slope. | Plug in the slope for "m" and the y-intercept for "b" | Use the slope equation with the points to get a slope, then pick one of the two points and follow as above. |
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| Other Equations: | ||||
| x = c | Vertical line | No Slope | ||
| y = c | Horizontal Line | Zero Slope | ||