Slope-Intercept Form (y = mx + b)

The most common way to write a linear equation is slope-intercept form: [formula] where: - m = slope (rate of change) - b = y-intercept (where the line crosses the y-axis) This form is powerful because you can read the slope and y-intercept directly from the equation without any calculation.

Example: Identify the slope and y-intercept of y = 3x - 4.

If you know the slope and one point on the line, you can write the equation: 1. Start with y = mx + b 2. Plug in m (slope) and the point (x, y) 3. Solve for b 4. Write the final equation

Example: Write the equation of a line with slope 4 that passes through (2, 11).

To graph y = mx + b: 1. Plot the y-intercept (0, b) 2. Use the slope to find a second point: from (0, b), go right by the run and up/down by the rise 3. Draw the line through the two points Example: For y = frac{2}{3}x - 1: 1. Plot (0, -1) 2. From there, go right 3, up 2 → plot (3, 1) 3. Draw the line

Many SAT questions give an equation in non-standard form and ask for slope or y-intercept. Always rearrange to y = mx + b first — it takes 10 seconds and makes the answer obvious. Also, when matching a graph to an equation, check the y-intercept first (it's the quickest check) then verify the slope.