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10.5 Writing Slope-Intercept Equations of Lines

10.5 Writing Slope-Intercept Equations of Lines. CORD Math Mrs. Spitz Fall 2006. Objectives:. Write a linear equation in slope-intercept form given the slope of a line and the coordinates of a point on the line, and

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10.5 Writing Slope-Intercept Equations of Lines

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  1. 10.5 Writing Slope-Intercept Equations of Lines CORD Math Mrs. Spitz Fall 2006

  2. Objectives: • Write a linear equation in slope-intercept form given the slope of a line and the coordinates of a point on the line, and • Write a linear equation in slope-intercept form given the coordinates of two points on the line.

  3. Assignment • Pgs. 421-422 #4-31 all

  4. Application • The present population of Cedarville is 55,000. If the population increases by 600 people each year, the equation y = 600x + 55,000 can be used to find the population x years from now. Notice that 55,000 is the y-intercept and 600 (the growth per year) is the slope.

  5. Application continued • In the problem above, the slope and y-intercept were used to write an equation. Other information can also be used to write an equation for a line. In fact, given any one of the three types of information below about a line, you can write an equation for a line. • The slope and a point on the line • Two points on a line • The x- and y-intercepts

  6. Ex. Write an equation of whose slope is 3 that passes through (4, -2). y = mx + b Use slope-intercept form y = 3x + b The slope is 3 -2 = 3(4) + b Substitute 4 for x and -2 for y -2 = 12 + b Solve for b -14 = b The slope-intercept form of the equation of the line is y = 3x + (-14) or y = 3x – 14.

  7. Ex. Write an equation of whose slope is 3 that passes through (4, -2). The slope-intercept form of the equation of the line is y = 3x + (-14) or y = 3x – 14. In standard form: y = 3x – 14 Slope-intercept form -3x + y = -14 Subtract x from both sides 3x – y = 14 Multiply by -1 to change the sign of the leading coefficient in front of x.

  8. What about the equation with 2 points? • Example 2 illustrates a procedure that can be used to write an equation of a line when two points on the line are known. • Write an equation in slope-intercept form of the line that passes through each pair of points: (-1, 7), (8, -2) • First determine the slope of the line

  9. Ex. 2 continued (-1, 7), (8, -2) are the two points. m = -1 y = mx + b slope intercept form y = -1x + b substitute -1 for m 7 = -1(-1) + b substitute 7 for y and -1 for x 7 = 1 + b Distribute 6 = b Solve for b Equation of the line is y = -x + 6

  10. Ex. 3: Write an equation of the line that passes through (7.6, 10.8) and (12.2, 93.7). Round values to the nearest thousandth. Start with slope y = mx + b Slope-intercept form y = 18.022x + b Substitute 18.022 for slope, m Substitute 10.8 for y and 7.6 for x 10.8 = 18.022(7.6) + b Distribute/simplify 10.8 = 136.967 + b Subtract 136.067 from both sides -126.167 = b Equation of the line is y = 18.022x – 126.167

  11. So you could just look at the graph and count, right? Rise over run. You know its negative because of the way it’s facing. So count. Ex. 4: Write an equation for line PQ whose graph is shown below. 1, 2 , 3 , 4 down 1, 2 , 3 over to the right -4/3 right?

  12. You could also use the slope formula with the points (0, 4) and (3, 0) Ex. 4: Write an equation for line PQ whose graph is shown below. Simply a matter of following the formula from there.

  13. Ex. 4: Write an equation for line PQ whose graph is shown below. • Points (0, 4) and (3, 0) y = mx + b Rewrite the equation as: Rewrite the equation in standard form as follows:

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