Graphing Linear Equations Cheat Sheet

Equation

y = mx + b, where m is the slope and b is the y-intercept.

Example: y = 2x + 3 (slope is 2, y-intercept is 3)

Slope (m)

The rate of change of the line (rise over run).

Example: If m = 1/2, for every 2 units you move to the right, you move 1 unit up.

Y-intercept (b)

The point where the line crosses the y-axis (x=0).

Example: In y = 2x + 3, the line crosses the y-axis at (0, 3).

Graphing from Slope-Intercept Form

1. Plot the y-intercept (0, b). 2. Use the slope (m) to find another point. 3. Draw a line through the two points.

Example: For y = (1/3)x - 2, plot (0, -2). Then, from that point, go up 1 and right 3 to find another point. Draw the line.

Equation

y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is a point on the line.

Example: y - 5 = 3(x - 2) (slope is 3, point is (2, 5))

Using Point-Slope Form

1. Identify the slope (m) and a point (x₁, y₁). 2. Substitute the values into the equation. 3. Simplify to slope-intercept form (optional).

Example: Given slope 2 and point (1, 4): y - 4 = 2(x - 1). Simplifying gives y = 2x + 2.

Graphing from Point-Slope Form

1. Plot the given point (x₁, y₁). 2. Use the slope (m) to find another point. 3. Draw a line through the two points.

Example: For y - 1 = -2(x + 3), plot (-3, 1). Then, from that point, go down 2 and right 1 to find another point. Draw the line.

Equation

Ax + By = C, where A, B, and C are constants.

Example: 2x + 3y = 6

Finding Intercepts

To find the x-intercept, set y = 0 and solve for x. To find the y-intercept, set x = 0 and solve for y.

Example: For 2x + 3y = 6: x-intercept is (3, 0), y-intercept is (0, 2).

Graphing from Standard Form

1. Find the x and y intercepts. 2. Plot the intercepts. 3. Draw a line through the intercepts.

Example: For 4x - 2y = 8, plot (2, 0) and (0, -4). Draw the line.

Converting to Slope-Intercept Form

Solve the equation for y to get it into y = mx + b form.

Example: For 2x + y = 5, subtract 2x from both sides to get y = -2x + 5.