Slope-Intercept Form Basics

The slope-intercept form of a line is written as y=mx+b. In this equation, m represents the slope (how steep the line is), and b is the y-intercept $where the line crosses the y-axis$.

Finding these values is easy when the equation is already in this form. For example, in y=3x+2, the slope is 3 and the y-intercept is 2. In y=¼x-1, the slope is ¼ and the y-intercept is -1.

Sometimes equations aren't in this form yet. When that happens, you need to rearrange them. For 2y=8x+10, divide everything by 2 to get y=4x+5, giving a slope of 4 and y-intercept of 5. For 7x+y=8, subtract 7x from both sides to get y=8-7x or y=-7x+8.

Try This! When graphing a line like y=-2x+3, first mark the y-intercept (0,3) on your graph, then use the slope to find your next point by going down 2 and right 1.

To graph a line in slope-intercept form:

1. Plot the y-intercept on the y-axis first
2. Use the slope as directions to find your next point
3. Remember: The numerator tells you to go up (positive) or down (negative), and the denominator always tells you to go right

For example, if your slope is ⅔, go up 2 and right 3 from your y-intercept. If it's -5, go down 5 and right 1. Connect the points, and you've got your line!