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Objective The student will be able to: <ul><li>Graph linear equations in slope- intercept form.  </li></ul><ul><li>write e...
Remember
FORMULA FOR FINDING SLOPE The formula is used when you know two points of a line.  EXAMPLE
Find the slope of the line between the two points (-4, 8) and (10, -4) If it helps label the points. Then use the formula
Graphing Linear Equations In Slope-Intercept Form
We have already seen that linear equations have two variables and when we plot all the (x,y) pairs that make the equation ...
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).  <ul><li>The  constant  is the  y-intercept...
The formula for Slope-Intercept Form is:  <ul><li>‘ b’  is the  y-intercept .  </li></ul><ul><li>‘ m’  is the  slope . </l...
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 c...
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...
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...
<ul><li>Sometimes we must solve the equation for  y  before we can graph it. </li></ul>The constant,  b = 3  is the y-inte...
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 c...
Important!!! This is one of the big concepts in  Algebra 1. You need to thoroughly understand this! Slope – Intercept Form...
Writing Equations When asked to write an equation, you need to know two things – slope (m) and y-intercept (b). There are ...
Writing Equations – Type #1 Write an equation in slope-intercept form of the line that has a slope of 2 and a y-intercept ...
Write the equation of a line that has a y-intercept of -3 and a slope of -4. <ul><li>y = -3x – 4 </li></ul><ul><li>y = -4x...
Writing Equations – Type #2 Write an equation of the line that has a slope of 3 and goes through the point (2,1). To write...
Writing Equations – Type #2 1 = 3(2) + b Solve the equation for b   1 = 6 + b   -6  -6 -5 = b To write an equation, you ne...
Writing Equations – Type #3 <ul><li>Write an equation of the line that goes through the points (-2, 1) and (4, 2).  </li><...
Writing Equations – Type #3 <ul><li>Write an equation of the line that goes through the points (-2, 1) and (4, 2).  </li><...
Writing Equations – Type #3 2  =  (4)  + b Solve the equation for b   2 =  + b   To write an equation, you need two things...
Write an equation of the line that goes through the points (0, 1) and (1, 4). <ul><li>y = 3x + 4 </li></ul><ul><li>y = 3x ...
To find the slope and y-intercept of an equation, write the equation in slope-intercept form: y = mx + b. <ul><li>Find the...
Find the slope and y-intercept. <ul><li>2) y =  x </li></ul><ul><li>y =  m x +  b </li></ul><ul><li>y =  x + 0 </li></ul><...
Find the slope and y-intercept. 4) 5x - 3y = 6 <ul><li>Write it in slope-intercept form. (y = mx + b) </li></ul><ul><li>5x...
<ul><li>Write it in slope-intercept form. (y = mx + b) </li></ul><ul><li>2y + 2 = 4x </li></ul><ul><li>  2y = 4x - 2 </li>...
Find the slope and y-intercept of  y = -2x + 4 <ul><li>m = 2; b = 4 </li></ul><ul><li>m = 4; b = 2 </li></ul><ul><li>m = -...
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Writing and Graphing slope intercept form

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Transcript of "Writing and Graphing slope intercept form"

  1. 1. Objective The student will be able to: <ul><li>Graph linear equations in slope- intercept form. </li></ul><ul><li>write equations using slope-intercept form. </li></ul><ul><li>identify slope and y-intercept from an equation. </li></ul>
  2. 2. Remember
  3. 3. FORMULA FOR FINDING SLOPE The formula is used when you know two points of a line. EXAMPLE
  4. 4. Find the slope of the line between the two points (-4, 8) and (10, -4) If it helps label the points. Then use the formula
  5. 5. Graphing Linear Equations In Slope-Intercept Form
  6. 6. 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.
  7. 7. These equations are all in Slope-Intercept Form: Notice that these equations are all solved for y.
  8. 8. Just by looking at an equation in this form, we can draw the line (no tables). <ul><li>The constant is the y-intercept. </li></ul><ul><li>The coefficient is the slope . </li></ul>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.
  9. 9. The formula for Slope-Intercept Form is: <ul><li>‘ b’ is the y-intercept . </li></ul><ul><li>‘ m’ is the slope . </li></ul>On the next three slides we will graph the three equations: using their y-intercepts and slopes.
  10. 10. 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
  11. 11. 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
  12. 12. 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
  13. 13. <ul><li>Sometimes we must solve the equation for y before we can graph it. </li></ul>The constant, b = 3 is the y-intercept. The coefficient, m = -2 is the slope.
  14. 14. 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
  15. 15. Important!!! This is one of the big concepts in Algebra 1. You need to thoroughly understand this! Slope – Intercept Form y = mx + b m represents the slope b represents the y-intercept
  16. 16. Writing Equations When asked to write an equation, you need to know two things – slope (m) and y-intercept (b). There are three types of problems you will face.
  17. 17. Writing Equations – Type #1 Write an equation in slope-intercept form of the line that has a slope of 2 and a y-intercept of 6. To write an equation, you need two things: slope (m) = y – intercept (b) = We have both!! Plug them into slope-intercept form y = mx + b y = 2x + 6 2 6
  18. 18. Write the equation of a line that has a y-intercept of -3 and a slope of -4. <ul><li>y = -3x – 4 </li></ul><ul><li>y = -4x – 3 </li></ul><ul><li>y = -3x + 4 </li></ul><ul><li>y = -4x + 3 </li></ul>
  19. 19. Writing Equations – Type #2 Write an equation of the line that has a slope of 3 and goes through the point (2,1). To write an equation, you need two things: slope (m) = y – intercept (b) = We have to find the y-intercept!! Plug in the slope and ordered pair into y = mx + b 1 = 3(2) + b 3 ???
  20. 20. Writing Equations – Type #2 1 = 3(2) + b Solve the equation for b 1 = 6 + b -6 -6 -5 = b To write an equation, you need two things: slope (m) = y – intercept (b) = y = 3x - 5 3 -5
  21. 21. Writing Equations – Type #3 <ul><li>Write an equation of the line that goes through the points (-2, 1) and (4, 2). </li></ul><ul><li>To write an equation, you need two things: </li></ul><ul><li>slope (m) = </li></ul><ul><li>y – intercept (b) = </li></ul><ul><li>We need both!! First, we have to find the slope. Plug the points into the slope formula. </li></ul><ul><li>Simplify </li></ul>??? ???
  22. 22. Writing Equations – Type #3 <ul><li>Write an equation of the line that goes through the points (-2, 1) and (4, 2). </li></ul><ul><li>To write an equation, you need two things: </li></ul><ul><li>slope (m) = </li></ul><ul><li>y – intercept (b) = </li></ul><ul><li>It’s now a Type #2 problem. Pick one of the ordered pairs to plug into the equation. Which one looks easiest to use? </li></ul><ul><li>I’m using (4, 2) because both numbers are positive. </li></ul><ul><li>2 = (4) + b </li></ul>???
  23. 23. Writing Equations – Type #3 2 = (4) + b Solve the equation for b 2 = + b To write an equation, you need two things: slope (m) = y – intercept (b) =
  24. 24. Write an equation of the line that goes through the points (0, 1) and (1, 4). <ul><li>y = 3x + 4 </li></ul><ul><li>y = 3x + 1 </li></ul><ul><li>y = -3x + 4 </li></ul><ul><li>y = -3x + 1 </li></ul>
  25. 25. To find the slope and y-intercept of an equation, write the equation in slope-intercept form: y = mx + b. <ul><li>Find the slope and y-intercept. </li></ul><ul><li>y = 3x – 7 </li></ul><ul><li>y = m x + b </li></ul><ul><li>m = 3, b = -7 </li></ul>
  26. 26. Find the slope and y-intercept. <ul><li>2) y = x </li></ul><ul><li>y = m x + b </li></ul><ul><li>y = x + 0 </li></ul><ul><li>3) y = 5 </li></ul><ul><li>y = m x + b </li></ul><ul><li>y = 0x + 5 </li></ul>m = b = 0 m = 0 b = 5
  27. 27. Find the slope and y-intercept. 4) 5x - 3y = 6 <ul><li>Write it in slope-intercept form. (y = mx + b) </li></ul><ul><li>5x – 3y = 6 </li></ul><ul><li>-3y = -5x + 6 </li></ul><ul><li>y = x - 2 </li></ul>-3 -3 -3 m = b = -2
  28. 28. <ul><li>Write it in slope-intercept form. (y = mx + b) </li></ul><ul><li>2y + 2 = 4x </li></ul><ul><li> 2y = 4x - 2 </li></ul><ul><li>y = 2x - 1 </li></ul>Find the slope and y-intercept. 5) 2y + 2 = 4x 2 2 2 m = 2 b = -1
  29. 29. Find the slope and y-intercept of y = -2x + 4 <ul><li>m = 2; b = 4 </li></ul><ul><li>m = 4; b = 2 </li></ul><ul><li>m = -2; b = 4 </li></ul><ul><li>m = 4; b = -2 </li></ul>
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