1. Writing Equations in Point-Slope Form Algebra 1 Glencoe McGraw-Hill JoAnn Evans

2. Today we’re going to learn to use the Point-Slope form of the equation of a line. y – y 1 = m(x – x 1 ) Do any parts of this equation look familiar to you?

3. (3, 4).. (x, y) This graph shows a line with a slope of 2. Write an expression for the slope between the two points. Clear the fraction. Multiply both sides by (x – 3). Symetric Property This equation is written in Point-Slope form. y coordinate slope x coordinate

4.  m represents the slope of the line  (x 1, y 1 ) represents a known point on the line  (x, y) represents any other point on the line m, x 1, and y 1 will be replaced by numbers. x and y will be the variables.

5. Use the point-slope form to write the equation of the line passing through the point (-1, 3) with a slope of -2. Point-slope form The point-slope form has two subtraction signs in it. Don’t forget to include them if either x 1 or y 1 are negative numbers. -2 3

6. Write the equation of the line passing through the point (0, 7) with a slope of 12. Write the equation of the line passing through the point (-3, -4) with a slope of -2. When you’re asked to put an equation in Point-Slope form, don’t distribute the slope and isolate the y! Remember… in Point-Slope form, don’t distribute the slope and isolate the y!

7. Write the equation of the line passing through the point (-2, 0) with a slope of. Write the equation of the horizontal line passing through the point (0, 5). Horizontal lines have a slope of 0!

8. Change From Point-Slope to Slope-Intercept Form: Write an equation of the line that passes through the point (6, -8) with slope of -4. Then simplify the result to the slope-intercept form. Point-Slope equation Substitute -4 for m, 6 for x 1, and -8 for y 1 Subtract 8 from both sides Simplify and distribute Slope-Intercept Form! Point-Slope Form!

9. Write an equation of the line that passes through the point (5, -1) with slope of. Then simplify the result to the slope-intercept form. Slope-Intercept Form! Point-Slope Form!

10. Change From Point-Slope Form to Standard Form: Write the equation y + 6 = -3(x – 4) in standard form. Distribute the slope. Subtract 6 from both sides. Write the equation. Add 3x to both sides. Standard Form!

11. Change From Point-Slope Form to Standard Form: Write the equation in standard form. Multiply each side by 4 to clear the fraction. Write the equation. Subtract 20 from each side. Add 5x to both sides. Standard Form!

12. Acme Moving Company charges a set daily fee for renting a moving truck, plus a charge of $0.50 per mile driven. It cost Jordan $64 to rent the truck on a day when he drove a total of 48 miles. Write an equation in point-slope form to find the total fee, y, for any number of miles, x, that the truck is driven. What number represents a rate of change? $0.50 per mile This is the slope. (m) The instructions tell us that x will represent the number of miles and y will represent the total cost. (x, y) (48, 64) The # of miles is 48. The cost is $64.

13. Acme Moving Company charges a set daily fee for renting a moving truck, plus a charge of $0.50 per mile driven. It cost Jordan $64 to rent the truck on a day when he drove a total of 48 miles. We have enough information now to write an equation in point-slope form. m = 0.50 (48, 64) Change the equation from point-slope form to slope- intercept form. What is the daily fee to rent a truck?

14. In 1908 the average movie ticket cost $0.05! 100 years later in 2008 the average movie ticket cost $8.50! Use this information to write the point-slope form of an equation to find the cost of a movie ticket, y, for any year, x. In 1908: (year, cost) (0, 0.05) In 2008: (year, cost) (100, 8.50) Find the slope between the points: (100, 8.50) (0, 0.05)

15. What does this mean? This is the rate of change for the cost of a movie ticket over that period of 100 years. The cost rose, on average, 8.45 cents per year. Use the slope and one of the points to write an equation in point-slope form. Use (100, 8.50) Change this equation to slope-intercept form. Cost of a movie in year 0. Rate of change per year.

16. Use the equation to predict the price of a movie ticket 10 years from now. 10 years from now it will be 110 years since the 0 year. Substitute 110 for the year. If tickets keep rising at the same rate, it should cost about $9.35 to see a movie in 2018.