8.3 Slope And Y Intercept

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Chapter 8, Section 3: Slope and Y-Intercept.

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8.3 Slope And Y Intercept

  1. 1. Chapter 8 Section 3 Slope and Y-Intercept February 9 th , 2009 I suggest you write EVERY THING down in your notes.
  2. 2. Warm Up <ul><li>Solve for y: </li></ul><ul><li>9x + y = 7 </li></ul><ul><li>6x – 3y = 12 </li></ul><ul><li>11 – y = x </li></ul><ul><li>x = 14 – 7y </li></ul><ul><li>Write each ration in Simplest Form. </li></ul><ul><li>(8-2)/(5-3) </li></ul><ul><li>(1-3)/(6-0) </li></ul><ul><li>(6 – (-2))/(5 – 9) </li></ul><ul><li>(-2 – (-3))/(7 – 10) </li></ul>
  3. 3. Slope <ul><li>The ratio that describes the tilt of a line is its slope. </li></ul><ul><li>To calculate slope, you use this ratio. </li></ul><ul><li>Slope = (Vertical Change)/(Horizontal Change) </li></ul><ul><li>Slope = Rise/Run (Rise over Run). </li></ul>
  4. 4. Slope <ul><li>Rise shows vertical change. </li></ul><ul><li>Run shows horizontal change. </li></ul><ul><li>Up means positive. </li></ul><ul><li>Down means negative. </li></ul><ul><li>Right is positive. </li></ul><ul><li>Left is negative. </li></ul>
  5. 5. Find the Slope of Each Line <ul><li>Remember: Rise over Run. </li></ul>Rise: 2 Run: 4 Rise: -3 Run: 2 Ratio is 2 / 4 Ratio is -3 / 2 We’re reading from left to right. So start at the left most point and then figure out how to get to the next point.
  6. 6. If You Know Two Points: <ul><li>You can find the slope of the line using the ratio. </li></ul><ul><li>The difference of y – coordinates OVER the difference of x – coordinates. </li></ul><ul><li>The y -coordinate you use first in the numerator must correspond to the x -coordinate you use first in the denominator. </li></ul><ul><li>P.S.: Difference means to subtract! </li></ul>
  7. 7. Find the slope of the line through C( -2, 6 ) and D( 4, 3 ). <ul><li>Slope = difference in y-coordinates </li></ul><ul><li>difference in x-coordinates </li></ul><ul><li>= ( 3 – 6 )  y-coordinates </li></ul><ul><li>( 4 – ( -2 ))  x-coordinates </li></ul><ul><li>Slope = -3 / 6 = -1/2 </li></ul><ul><li>Down 1, to the Right 2. Cause of Rise (of –1) over Run (+2). </li></ul>
  8. 8. Find the Slope of the Line through each pair of points: <ul><li>V(8, -1) and Q(0, -7) </li></ul><ul><li>S(-4, 3) and R(-10, 9) </li></ul>3/4: Rise = 3, Run = 4 -1 or (1/-1): Rise = 1, Run = -1
  9. 9. X = ? And Y = ?, Are Special. <ul><li>Horizontal and Vertical lines are special cases for slope. </li></ul>This is a horizontal line. The points are (-3, 2) and (1, 2). Therefore, Y = 2. Find the slope. Slope = (2 – 2) / (1 – (-3) = 0 /4 = 0 The slope for a horizontal line (or anything Y = ?) is zero.
  10. 10. X = ? And Y = ?, Are Special. <ul><li>Horizontal and Vertical lines are special cases for slope. </li></ul>This is a vertical line. The points are (-4, 1) and (-4, 3). Therefore, X = -4. Find the slope. Slope = (1 – 3) / (-4 – (-4) = -2 /0 = Undefined Division by zero is undefined. (Zero as the denominator). Slope is, therefore, UNDEFINED for vertical lines .
  11. 11. Word Problem <ul><li>A store sells sugar in bulk for 25 cents per pound. </li></ul><ul><li>Graph the relation (pound of sugar, cost). </li></ul><ul><li>Draw a line through the points on your graph and find its slope. </li></ul>
  12. 12. Using Slope to Graph Linear Equations <ul><li>This is the graph of y=(-1/2)x + 3. </li></ul><ul><li>The slope of the line is (-2/4) or (-1/2). </li></ul><ul><li>The Y-INTERCEPT of the line is the point where the line crosses the Y-AXIS. </li></ul><ul><li>The CONSTANT in the equation is the same as the y-intercept . </li></ul>
  13. 13. Using Slope to Graph Linear Equations <ul><li>This is the graph of y=(-1/2)x + 3. </li></ul><ul><li>The slope of the line is (-2/4) or (-1/2). </li></ul>y = (-1/2) x + 3 Slope = always a ratio Y-Intercept = Constant
  14. 14. Slope-Intercept Form <ul><li>Using the Slope-Intercept Form, you can graph without having to pick points and make a table. </li></ul><ul><li>y = mx + b = Slope-Intercept Form </li></ul><ul><li>M = Slope of the line. (Ratio) </li></ul><ul><li>B = Y-Intercept. (Constant) </li></ul><ul><li>Linear Equations will always be in this format, or at least, be able to be made into this format. Like solving for y. </li></ul>
  15. 15. To Graph with y = mx + b <ul><li>Start with b. Since b is where the line of the equation hits the y-axis, its your first point. Point = (0, b) </li></ul><ul><li>Take the slope, or m. Starting at b, move along the RISE and RUN of the ratio. </li></ul><ul><li>Where you end up is your second point. </li></ul><ul><li>Connect the two dots with a line. (This is the graph of your linear equation). </li></ul>
  16. 16. Lets Graph Together! <ul><li>y = (-1/3)x + 2 </li></ul><ul><li>If you can’t tell where the negative goes, always put it on the numerator. </li></ul><ul><li>b = 2 so, (0, 2) </li></ul><ul><li>Rise: -1, Run: +3 </li></ul><ul><li>Graph next dot. </li></ul><ul><li>Connect dots with straight line. </li></ul>
  17. 17. Assignment #3 <ul><li>Pages 400-401: 1-41 odd numbered problems. </li></ul>

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