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The Slope-Intercept Form of an Equation


Introduction

Slope-intercept_form_vis_1


Consider the line that is drawn to the left.  One way to describe it with an equation is to figure out the slope and the y-intercept of the line.  These two pieces of information (the slope and the y-intercept) allow you to write the equation of the line.  Since the equation describes the slope and the y-intercept of the line, is said to be written in slope-intercept form.

 

 

The slope-intercept form of an equation is y = mx + b, where m is the slope and b is the y-intercept.


Lesson

Slope-intercept_form_vis_2Any linear equation can be written in the form y = mx + b, where m is the slope and b is the y-intercept.  This equation is a simple way to compare the x and y values of any line on the coordinate plane.   

 

The two equations below are in slope-intercept form.  Compare the two equations to their corresponding graphs to get an idea of how the slope and position of the line changes based on the slope and y-intercept in the equation. 

Slope-intercept_form_vis_3Slope-intercept_form_vis_4 

 

When a line is written in slope-intercept form, it is possible to graph the line by starting at the y-intercept and then using the slope value to find other points to the right and left.

 

 

Slope-intercept_form_vis_5aExample 1:  Draw the graph of the line y = 3x – 5

 

Solution:

 

Step 1: The y-intercept is -5, so plot the point (0, -5)

 

 

Step 2: The slope is 3, so add a second point by moving up 3 units and right 1 unit.  The second point is (1, -2)

 

Step 3: Plot a third point by moving up 3 units and right 1 unit from the second point.  The third point is (2, 1).

 

Step 4: Draw a line though the points. 

 

 

 

Slope-intercept_form_vis_6

Drawing three points is a good idea because you will draw a more accurate line than you would with only two points.  Plotting three separate points gives your line better definition and ensures that you have not made a math error.  If the three points are not collinear, then and check each coordinate again.

 

  

Slope-intercept_form_vis_8aExample 2: Draw the graph of the line Slope-intercept_form_vis_7 

 

Solution:

 

Step 1:  The y-intercept is 1, so plot the point (0, 1)

 

Step 2:  The slope is 2/3, so add a second point by moving up 2 units and right 3 units.  The second point is (3, 3)

 

Step 3:  Plot a third point by moving up 2 units and right 3 units from the second point.  The third point is (6, 5).

 

Step 4:  Draw a line though the points. 

 

 

 

Slope-Intercept Equations and T-Charts

The examples that we have looked at so far compare the slope-intercept equation with the corresponding graph of a line.  The one piece of information that was not included was the t-chart of the line.  A t-chart is simply a chart that is used to list a number of coordinates of an equation.  These coordinates can then be used to draw the graph of the equation.

Consider the equation y = -2x + 5.  This equation can be compared to the t-chart and graph as follows:

 

Slope-intercept_form_vis_9 

 

The slope of this line is -2 and the y-intercept is the coordinate (0, 5).  The three red -2’s next to the t-chart come from the slope of the equation.  Since the slope is -2, the y-value decreases by 2 when the x-value goes up by 1. 

 

 

Try It

Find the slope and y-intercept for each equation:

1) y = x + 5 

2) y = 4x + 6

3) y = -½x + 5  

4)  y = -6x

5)  y = -2 

 

 

Find the equation of each line below:

6)  Slope-intercept_form_vis_10 

 

7)  Slope-intercept_form_vis_11 

 

 


Scroll down for answers…

 

 

  

  

  

  

 

 

Answers:

 

 1)  Slope is 1 and y-intercept is 5   (Equation: y = x + 5)

 2)  Slope is 4 and y-intercept is 6   (Equation: y = 4x + 6)

 3)  Slope is -½  and y-intercept is 5   (Equation: y = -½x + 5)

4)  Slope is -6 and y-intercept is 0   (Equation: y = -6x  or y = -6x + 0)

5)  Slope is 0 and y-intercept is -2   (Equation:  y = -2)

6)  Slope-intercept_form_vis_12 

7)  Slope-intercept_form_vis_13

 

 

 

Related Links:

For more information on slope-intercept form and related topics, try one of the links below.

 

Resource Pages

 

Related Lessons

 

Looking for something else?  Try the general math or algebra lesson links.

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