4-7 Point-Slope Form. Warm Up Lesson Presentation Lesson Quiz

Transcription

1 Warm Up Lesson Presentation Lesson Quiz Holt Algebra McDougal 1 Algebra 1

2 Warm Up Find the slope of the line containing each pair of points. 1. (0, 2) and (3, 4) 2. ( 2, 8) and (4, 2) 1 3. (3, 3) and (12, 15) 2 Write the following equations in slope-intercept form. 4. y 5 = 3(x + 2) y = 3x x + 4y + 20 = 0

3 Objectives Graph a line and write a linear equation using point-slope form. Write a linear equation given two points.

4 If you know the slope and any point on the line, you can write an equation of the line by using the slope formula. For example, suppose a line has a slope of 3 and contains (2, 1). Let (x, y) be any other point on the line. Substitute into the slope formula. Multiply both sides by (x - 2). Simplify.

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6 Additional Example 1A: Writing Linear Equations in Point-Slope Form Write an equation in point slope form for the line with the given slope that contains the given point. y y 1 = m (x x 1 ) Write the point-slope form.

7 Additional Example 1B: Writing Linear Equations in Point-Slope Form Write an equation in point slope form for the line with the given slope that contains the given point. slope = 4; (0, 3) y y 1 = m(x x 1 ) y 3 = 4(x 0) Write the point-slope form. Substitute 4 for m, 0 for x 1 and 3 for y 1. y 3 = 4(x 0)

8 Example 1C Write an equation in point slope form for the line with the given slope that contains the given point. slope = 0; (3, 4) y y 1 = m(x x 1 ) y ( 4) = 0(x 3) y + 4 = 0(x 3) Write the point-slope form. Substitute 0 for m, 3 for x 1 and 4 for y 1. Rewrite subtraction of negative numbers as addition.

9 Additional Example 2A: Writing Linear Equations in Slope-Intercept Form Write the equation that describes each line in slope-intercept form. Slope = 3, ( 1, 4) is on the line. Step 1 Write the equation in point-slope form: y 4 = 3[x ( 1)] Step 2 Write the equation in slope-intercept form by solving for y. y y 1 = m(x x 1 ) y 4 = 3(x + 1) y 4 = 3x y = 3x + 7 Rewrite subtraction of negative numbers as addition. Distribute 3 on the right side. Add 4 to both sides.

10 Additional Example 2B: Writing Linear Equations in Slope-Intercept Form Write the equation that describes the line in slope-intercept form. (2, 3) and (4, 1) Step 1 Find the slope. Step 2 Substitute the slope and one of the points into the point-slope form. y y 1 = m(x x 1 ) y ( 3) = 2(x 2) Choose (2, 3).

11 Additional Example 2B Continued Write an equation in slope-intercept form for the line through the two points. (2, 3) and (4, 1) Step 3 Write the equation in slope-intercept form. y + 3 = 2(x 2) y + 3 = 2x y = 2x 7

12 Example 2C Write the equation that describes the line in slope-intercept form. Step 1 Write the equation in point-slope form: y y 1 = m(x x 1 )

13 Example 2C Continued Write an equation in slope-intercept form for the line with slope that contains ( 3, 1). Step 2 Write the equation in slope-intercept form by solving for y. Rewrite subtraction of negative numbers as addition. Distribute on the right side Add 1 to both sides.

14 Example 2D Write an equation in slope-intercept form for the line through the two points. (1, 2) and (3, 10) Step 1 Find the slope. Step 2 Substitute the slope and one of the points into the point-slope form. y y 1 = m(x x 1 ) y ( 2) = 6(x 1) Choose (1, 2). y + 2 = 6(x 1)

15 Example 2D Continued Write an equation in slope-intercept form for the line through the two points. (1, 2) and (3, 10) Step 3 Write the equation in slope-intercept form. y + 2 = 6(x 1) y + 2 = 6x Distribute 6 on the right side. Subtract 2 from both sides. y = 6x 8

16 Example 3: Problem-Solving Application The cost to stain a deck is a linear function of the deck s area. The cost to stain 100, 250, 400 square feet are shown in the table. Write an equation in slope-intercept form that represents the function. Then find the cost to stain a deck whose area is 75 square feet.

17 Example 3 Continued 1 Understand the Problem The answer will have two parts an equation in slope-intercept form and the cost to stain an area of 75 square feet. The ordered pairs given in the table (100, 150), (250, ), (400, 525) satisfy the equation.

18 2 Make a Plan Example 3 Continued You can use two of the ordered pairs to find the slope. Then use point-slope form to write the equation. Finally, write the equation in slope-intercept form.

19 Example 5 Continued 3 Solve Step 1 Choose any two ordered pairs from the table to find the slope. Use (100, 150) and (400, 525). Step 2 Substitute the slope and any ordered pair from the table into the point-slope form. y y 1 = m(x x 1 ) y 150 = 1.25(x 100) Use (100, 150).

20 3 Solve Step 3 Write the equation in slope-intercept form by solving for y. Example 3 Continued y 150 = 1.25(x 100) y 150 = 1.25x 125 Distribute y = 1.25x + 25 Add 150 to both sides. Step 4 Find the cost to stain an area of 75 sq. ft. y = 1.25x + 25 y = 1.25(75) + 25 = The cost of staining 75 sq. ft. is $

21 Example 3 Continued 4 Look Back If the equation is correct, the ordered pairs that you did not use in Step 2 will be solutions. Substitute (400, 525) and (250, ) into the equation. y = 1.25x (400) y = 1.25x (250)

22 Lesson Quiz: Part I Write an equation in slope-intercept form for the line with the given slope that contains the given point. 1. Slope = 1; (0, 9) y 9 = (x 0) 2. Slope = ; (3, 6) y + 6 = (x 3) Write an equation that describes each line the slope-intercept form. 3. Slope = 2, (2, 1) is on the line y = 2x (0, 4) and ( 7, 2) are on the line y = x + 4

23 Lesson Quiz: Part II 5. The cost to take a taxi from the airport is a linear function of the distance driven. The cost for 5, 10, and 20 miles are shown in the table. Write an equation in slope-intercept form that represents the function. y = 1.6x + 6