Linear Equations Cheat Sheet

Standard FormSlope 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.

Other Equations:

x = c Vertical line No Slope

y = c Horizontal Line Zero Slope

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