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We have already seen that linear equations have two variables and when we plot all the (x,y) pairs that make the equation true we get a  line .  In this section, instead of making a table, evaluating y for each x, plotting the points and making a line, we will use  The Slope-Intercept  Form of the equation to graph the line.
These equations are all in  Slope-Intercept Form:  Notice that these equations are all solved for y.
Just by looking at an equation in this form, we can draw the line (no tables).  ,[object Object],[object Object],Constant = 1, y-intercept = 1. Coefficient = 2, slope = 2. Constant = -4, y-intercept = -4. Coefficient = -1, slope = -1. Constant = -2, y-intercept = -2. Coefficient = 3/2, slope = 3/2.
The formula for Slope-Intercept Form is:  ,[object Object],[object Object],On the next three slides we will graph the three equations:  using their y-intercepts and slopes.
1)  Plot the y-intercept as a point on the y-axis.  The constant, b = 1, so the y-intercept = 1. 2)  Plot more points by counting the slope up the numerator (down if negative) and right the denominator.  The coefficient, m = 2, so the slope = 2/1. up 2 right 1 up 2 right 1
1)  Plot the y-intercept as a point on the y-axis.  The constant, b = -4, so the y-intercept = -4. 2)  Plot more points by counting the slope up the numerator (down if negative) and right the denominator.  The coefficient, m = -1, so the slope = -1/1. right 1 down 1 right 1 down 1
1)  Plot the y-intercept as a point on the y-axis.  The constant, b = -2, so the y-intercept = -2. 2)  Plot more points by counting the slope up the numerator (down if negative) and right the denominator.  The coefficient, m = 3/2, so the slope = 3/2. right 2 up 3 right 2 up 3
[object Object],The constant,  b = 3  is the y-intercept. The coefficient,  m = -2  is the slope.
1)  Plot the y-intercept as a point on the y-axis.  The constant, b = 3, so the y-intercept = 3. 2)  Plot more points by counting the slope up the numerator (down if negative) and right the denominator.  The coefficient, m = -2, so the slope = -2/1. right 1 down 2 right 1 down 2
The slope-intercept form of an equation gives you a quick way to graph the equation. Find  y -intercept, use it to plot point where line crosses y -axis. Find slope, use it to plot a second point on line. Draw line through points. Write equation in slope-intercept form by solving for  y . Click on the controller to practice G RAPHING  E QUATIONS IN  S LOPE- I NTERCEPT  F ORM S LOPE- I NTERCEPT  F ORM STEP   1 STEP   2 STEP   3 STEP   4

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Slope Powerpoint

  • 1.  
  • 2. We have already seen that linear equations have two variables and when we plot all the (x,y) pairs that make the equation true we get a line . In this section, instead of making a table, evaluating y for each x, plotting the points and making a line, we will use The Slope-Intercept Form of the equation to graph the line.
  • 3. These equations are all in Slope-Intercept Form: Notice that these equations are all solved for y.
  • 4.
  • 5.
  • 6. 1) Plot the y-intercept as a point on the y-axis. The constant, b = 1, so the y-intercept = 1. 2) Plot more points by counting the slope up the numerator (down if negative) and right the denominator. The coefficient, m = 2, so the slope = 2/1. up 2 right 1 up 2 right 1
  • 7. 1) Plot the y-intercept as a point on the y-axis. The constant, b = -4, so the y-intercept = -4. 2) Plot more points by counting the slope up the numerator (down if negative) and right the denominator. The coefficient, m = -1, so the slope = -1/1. right 1 down 1 right 1 down 1
  • 8. 1) Plot the y-intercept as a point on the y-axis. The constant, b = -2, so the y-intercept = -2. 2) Plot more points by counting the slope up the numerator (down if negative) and right the denominator. The coefficient, m = 3/2, so the slope = 3/2. right 2 up 3 right 2 up 3
  • 9.
  • 10. 1) Plot the y-intercept as a point on the y-axis. The constant, b = 3, so the y-intercept = 3. 2) Plot more points by counting the slope up the numerator (down if negative) and right the denominator. The coefficient, m = -2, so the slope = -2/1. right 1 down 2 right 1 down 2
  • 11. The slope-intercept form of an equation gives you a quick way to graph the equation. Find y -intercept, use it to plot point where line crosses y -axis. Find slope, use it to plot a second point on line. Draw line through points. Write equation in slope-intercept form by solving for y . Click on the controller to practice G RAPHING E QUATIONS IN S LOPE- I NTERCEPT F ORM S LOPE- I NTERCEPT F ORM STEP 1 STEP 2 STEP 3 STEP 4