Slope-Intercept Form

Slope-Intercept Form: y = mx + b

Converting to Slope-Intercept Form

To convert equation to Slope-intercept form: Solve the equation for y (get y by itself).

Examples:

1) Change to Slope-intercept form

Solve for y. To do this:

- Add both sides of the equation by 2y

- The - 2y and 2y cancel out

+ 2y + 2y 2y is added to the other side

- Subtract 10 to both sides of the equation

-10 -10 (Why do we do this? To get y on one side by itself.)

- Divide both sides by 2 to get y by itself

- The equation is now in slope-intercept form since y is by itself

2) Change to Slope-intercept form

- Solve for y (get y by itself)

- Subtract -3y to both sides

-3y -3y

- Add 9 to both sides

+9 +9

- Divide -3 on both sides to get y by itself

- Equation is now in slope-intercept form since y is by itself

Graphing Slope-intercept form

Slope-Intercept Form: y = mx + b

b: y-intercept

m: Slope

*The y-intercept is where the line crosses the y axis

*Slope = (Rise over Run)

1 is the rise 2 is the run

What is slope used for?

Slope is used to find the next point on the line.

If the slope is POSITIVE the line goes UPWARDS.

If the slope is NEGATIVE the line goes DOWNWARDS.

Examples:

1) Graph.

- Identify the slop and y-intercept

Slope: 4

Y-intercept:-5

- Plot the y-intercept -5

- Use to the slope to find the other points on the line.

- Connect the points to get the line of

2) Graph

- Identify the slope and y-intercept

Slope:

y-intercept: -3

- Plot the y-intercept -3

- Use to the slope to find the other points on the line.

- Connect the points to get the line of

Horizontal and Vertical Lines

When the equation has no slope the line is either horizontal or vertical.

Horizontal and Vertical lines both have no slope, making it a straight line.

Examples:

Graph

1) y = 1

- Find y-intercept at 1 and draw the line.

2) x = 1

- Find the x-intercept at 1 and draw the line.

Note: When graphing an equation such as y = 1,

the line must be parallel to the y axis.

When graphing an equation such as x = 1,

the line must be parallel the x axis.

Practice Problems

Change to slope-intercept form and graph.

1) 2)

Graph.

3) 4)

5) 6)