2. 10.5 Writing Slope- Intercept Equations of Lines CORD Math Mrs. Spitz Fall 2006

3. SLIDE 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.

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

5. SLIDE 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.

6. SLIDE 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. 1.The slope and a point on the line 2.Two points on a line 3.The x- and y-intercepts

7. SLIDE 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.

8. SLIDE 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.

9. SLIDE 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

10. SLIDE 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

11. SLIDE 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 10.8 = 18.022(7.6) + b Substitute 10.8 for y and 7.6 for x 10.8 = 136.967 + b Distribute/simplify -126.167 = b Subtract 136.067 from both sides Equation of the line is y = 18.022x – 126.167

12. SLIDE 11 Ex. 4: Write an equation for line PQ whose graph is shown below. 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. 1, 2, 3, 4 down 1, 2, 3 over to the right -4/3 right?

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

14. SLIDE 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: