Another way to graph a line is to get it in slope-intercept form: *y = mx + b*, where

*m* is the **slope **of the line *b* is the **y-intercept**

Since we are given a point of the line, and the slope, we can find an infinite number of other points on the line and connect them.

*Remember: slope (m) is equal to the (change in y) / (change in x). Slope = "rise over run"*

## Slope-intercept form of a line: *y = mx + b*

Let's examine how to graph one of these equations: y = 2x + 1.

This is in slope-intercept form, so we know that the number in front of x is the slope (2), and that 1 is the y-intercept.

Start by plotting the y-intercept.

Next, since we know that the slope is , also known as , we know that another point will be two spaces up and one over (in the positive direction of course).

Finally, connect these points.

**Look Out:** when using slope-intercept form to graph lines, you must solve the equation for y, not x.

## Slope-intercept Form Practice:

Graph the equation y = -½x – 2. | |

The slope of the line is -½, which will mean that it slopes downhill and is not very steep since the absolute value of the slope (|-½| is ½) is pretty small. We also know that it crosses the y-axis at -2. We will start by plotting the y-intercept and then counting over to the next point using a slope of -½. Remember that slope equals rise/run, so this line changes 1 in the vertical direction for every 2 in the horizontal. Also, since it is a negative slope, make sure that you plot your points in the correct direction, downhill. | |

Graph the equation 2y = x. | |

Again, we will need to solve for y, since it is not in y = mx + b form. | | | *divide each side by 2* | | *remember that the coefficient in front of x is 1* | *or* | |
| |

Now we can see that the slope of the equations is ½, but where is *b*, the y-intercept? Can't find it? That's because it is 0; it's not necessary to write y = ½x + 0. Let's plot a y-intercept of 0 and use the slope of ½ to find a few other points. | |

Find the equation of the line in slope-intercept form. | |

Let's look carefully at the graph and see if we can find any important information…. Ok, have you looked at it? You have, great! Then you noticed that the y-intercept is 1. We can also find the slope by counting the change in the vertical and horizontal directions between the two points shown (1 in the vertical and 3 in the horizontal). That gives a slope of 1/3. | |

Now, using that information we know these things: b = 1 and m = 1/3 | |

All we need to do is plug them into our equation, y = mx + b. y = (1/3)x + 1 | |

Graph the equation: y = -x + 2.

Hint

remember that –x has a coefficient of -1

Answer

Graph the equation: y - ¼x = -1.

Hint

solve the equation for y by adding -¼x to each side

Answer

Write the equation of this line in slope-intercept form:

Answer

y = 1x + 0 or y = x