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# Slope Intercept Form

We have seen here when graphing linear relationships that the equation for a straight line can be given in the form y = mx + b. This form is known as the Slope Intercept Form and it is a most useful form as it immediately shows two important things about any straight line when graphed on a Cartesian plane; the slope m, and the y-intercept b.

There are other forms of the equation of a straight line and the examples below will show how to convert from these to the slope intercept form.

There is more here on the slope of a line so we will start by looking at the y-intercept.

## The y-intercept

The y-intercept is the point at which a straight line intersects the y-axis. At this intersection point the value of x is always 0 so the y-value can be found algebraically simply by substituting 0 for x in the equation that represents the line as the example below shows.

### Move that intercept!

Try the graph generator with different values for the y-intercept (and the slope too if you wish) to see the effect on the line.

Your browser does not support the HTML 5 Canvas.

Enter slope(m) and y-intercept(b) below then click Draw Line

Drawing equation y = 2x – 1

Click Draw Line to graph the equation

### Finding the y-intercept

As shown earlier, finding the y-intercept is straightforward if the equation of the line is given in slope intercept form. e.g. for a line with equation y = 3x – 7, the y-intercept is at point (0, -7). If the equation is given in a different form then it can require additional steps as the two examples below show:

## Slope Intercept Form

The equation of a straight line can be given in different forms. The form y = mx + b is the most common and is known as the Slope Intercept Form. It is not the only form though; for example the equation ax + by = c is shown in what is known as standard form.

Two benefits of the slope intercept form is that both the slope (m) and the y-intercept (b ) are immediately obvious. Let us convert the example above from standard form to slope intercept form:

## Worksheets

Use the worksheet(s) below for practice.