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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
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. General Formula for Slope Intercept Equation


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.
Picture of Vertical Line Graph

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)
Picture of Horizontal Line
Slope Intercept Form
Point Slope Form
Standard Form
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Slope?
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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? Slope intercept form of linear equation
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


Slope intercept form of graph of line 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
Slope Intercept Form of Line in graph


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

Answer
The slope of a horizontal line= 0, because the there is no rise!
Therefore, m = 0

b = y-intercept of the line = 1

Therefore, the equation of this line in slope intercept form is
    y = 0X + 1 y = 1
Slope Intercept Form of Line in graph


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