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.

**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:

#### Example #1

Find the y-intercept for line with equation3x + 4y = 12 | |

substitute 0 for x | (3 x 0) + 4y = 124 y = 12 |

Divide both sides by 4 to isolate y | 4y ÷ 4 = 12 ÷ 4y = 3 |

y-intercept is at point (0,3) |

#### Example #2

Find the y-intercept for line with equation5x + 7y = -14 | |

substitute 0 for x | (5 x 0) + 7y = -147 y = -14 |

Divide both sides by 7 to isolate y | 7y ÷ 7= -14 ÷ 7y = -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 = 12into Slope Intercept Form | |

subtract 3x from both sides | 3x – 3x + 4y = -3x + 12 4 y = -3x + 12 |

Divide both sides by 4 to isolate y | 4y ÷ 4= (-3x ÷ 4) + (12 ÷ 4)y = (-3/4)x + 3 = -0.75y x + 3 |

#### Example #2

Convert -5x + 2y = 15into Slope Intercept Form | |

add 5x to both sides | 5x – 5x + 2y = 5x + 15 2 y = 5x + 15 |

Divide both sides by 2 to isolate y | 2y ÷ 2= (5x ÷ 2) + (15 ÷ 2)y = (5/2)x + 7.5y = 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 = (3×5) + 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.

- Slope Intercept Form – e.g. y = mx + b (2-Pages)
- Converting to Slope Intercept Form – (2-Pages)