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# Slope Intercept Form

## A way to express the equation of a line

 Worksheet (Worksheet with answer key on this page's topic) Slope Intercept Form Calculator Slope Intercept Applet
The slope intercept form is probably the most frequently used way  to express equation of a line. To be able to use slope intercept form, all that you need to be able to do is 1) find the slope of a line and 2) find the y-intercept of a line.
Video Tutorial on Slope Intercept Form

## The Formula

In general, the slope intercept form assumes the formula: y= mx +b.

Examples:
• y=5x+3 is an example of the Slope Intercept Form and represents the equation of a line with a slope of 5 and and a y-intercept of 3 .

• y= −2x + 6 represents the equation of a line with a slope of −2 and and a y-intercept of 6 .

### Slope Intercept Equation of vertical and horizontal lines

Vertical Lines

#### The Equation of a vertical line is x = b

Since a vertical line goes straight up and down, its slope is undefined. Also, the x value of every point on a vertical line is the same. Therefore, whatever the x value is, is also the value of 'b'. For instance, the red line in the picture below is the graph of the x = 1.

Horizontal Lines

The equation of a horizontal line is y = b where b is the y-intercept.

Since the slope of a horizontal line is 0, the general formula for the standard form equation , y = mx + b becomes y= 0x +b y = b. Also,since the line is horizontal, every point on that line has the exact same y value. This y-value is therefore also the y-intercept. For instance, the red line in the picture below is the graph of the horizontal line y =1. (In depth lesson on the equation of a horizontal line)
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Practice Problems

What is the slope intercept form of the lines graphed below?

Step 1) What is the slope of the line below?
 Answer

Step 3) What is the slope-intercept form of this line's equation?
 Slope Intercept Form

Look at the picture of the graph below. Find the slope of this line, its y-intercept, then express the equation of this line in slope intercept form

What is the slope of the line on the left?
 Answer

 Answer

What is the slope intercept form of this line?
 Answer

What is the slope intercept form of the line pictured in the graph below?

 Answer

What is the slope intercept form of the line pictured in the graph below?

 Answer

Practice Problems
Write the slope intercept form for the lines below
Problem 1) A line with a slope of 2 and a y-intercept of 12
 Answer

Problem 2) A line with a slope of 3 and a y-intercept of -5
 Answer

Problem 3) A line with a slope of ½ and a y-intercept of 7
 Answer