Slope Intercept Form

The slope-intercept form of a linear equation is written as y = mx + b, where m represents the slope (how steep the line is) and b represents the y-intercept $where the line crosses the y-axis$. This form makes it super easy to identify these key features at a glance!

When given an equation like y = 4/5x + 5, you can immediately tell that the slope is 4/5 (meaning the line rises 4 units for every 5 units it moves right) and the y-intercept is 5 $the line crosses the y-axis at the point (0,5)$. Similarly, in y = -3x + 17, the slope is -3 and the y-intercept is 17.

To write your own equation in slope-intercept form, just plug the values into y = mx + b. For example, if the slope is 1/2 and the y-intercept is 9, your equation would be y = (1/2)x + 9. If the slope is -4 and the y-intercept is 4, you'd write y = -4x + 4.

Quick Tip: Remember that a negative slope means the line goes downhill from left to right, while a positive slope means it goes uphill!

To graph a line using slope-intercept form:

1. Plot the y-intercept on the y-axis
2. Use the slope to find additional points $move right/left and up/down$
3. Connect the points with a straight line

For example, to graph y = 2x + 3, start at the point (0,3), then use the slope of 2 to find more points by moving right 1 unit and up 2 units repeatedly.