# 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.

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

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:

#### Example #1

 Find the y-intercept for line with equation 3x + 4y = 12 substitute 0 for x (3 x 0) + 4y = 12 4y = 12 Divide both sides by 4 to isolate y 4y ÷ 4 = 12 ÷ 4 y = 3 y-intercept is at point (0,3)

#### Example #2

 Find the y-intercept for line with equation 5x + 7y = -14 substitute 0 for x (5 x 0) + 7y = -14 7y = -14 Divide both sides by 7 to isolate y 7y ÷ 7= -14 ÷ 7 y = -2 y-intercept is at point (0,-2)

## 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:

### Converting to Slope Intercept Form

#### Example #1

 Convert 3x + 4y = 12 into Slope Intercept Form subtract 3x from both sides 3x - 3x + 4y = -3x + 12 4y = -3x + 12 Divide both sides by 4 to isolate y 4y ÷ 4= (-3x ÷ 4) + (12 ÷ 4) y = (-3/4)x + 3 y = -0.75x + 3

#### Example #2

 Convert -5x + 2y = 15 into Slope Intercept Form add 5x to both sides 5x - 5x + 2y = 5x + 15 2y = 5x + 15 Divide both sides by 2 to isolate y 2y ÷ 2= (5x ÷ 2) + (15 ÷ 2) y = (5/2)x + 7.5 y = 2.5x + 7.5

### Solving Other Problems

 What is the equation of a line that passes through point (5,6) and has a slope of 3? Substitute (5,6) for x and y and 3 (slope) for m in the equation in slope intercept form (y = mx + b) 6 = (3x5) + b 6 - 15 = b b = -9 Use the values of m and b to write the equation y = 3x - 9

## Worksheets

Use the worksheet(s) below for practice.

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