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Chapter 4

Chapter 4 . 4-7 Point slope Form. Objectives. Graph a line and write a linear equation using point-slope form. Write a linear equation given two points. Slope formula.

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Chapter 4

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  1. Chapter 4 4-7 Point slope Form

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

  3. Slope formula • 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 3and contains (2, 1) . Let (x, y) be any other point on the line.

  4. Slope formula

  5. Point-slope formula

  6. Example#1 • Write an equation in point slope form for the line with the given slope that contains the given point.

  7. Example #2 • Write an equation in point slope form for the line with the given slope that contains the given point. • slope = 1; (–1, –4)

  8. Example#3 • Write an equation in point slope form for the line with the given slope that contains the given point.

  9. Student guided practice • Do problems 1-3 in your book page 279.

  10. Point-slope form • In previous lessons, you graphed a line given its equation in slope-intercept form. You can also graph a line when given its equation in point-slope form. Start by using the equation to identify a point on the line. Then use the slope of the line to identify a second point.

  11. Example#4 • Graph the line described by the equation. • y – 1 = 2(x – 3) • Solution: • y – 1= 2(x – 3) is in the form • y – y1= m(x – x1). • The line contains the point (3, 1).

  12. SolutionExample#4 • Step 1 Plot (3, 1). • Step 2 Count 2 units upand 1 unit rightand plot another point. • Step 3 Draw the line connecting the two points.

  13. Example#5 • Graph the line described by the equation.

  14. Solution to Example#5 • Step 1 Plot (–2, 4). • Step 2 Count 3 unitsupand 4 units rightand plot another point. • Step 3 Draw the line connecting the two points.

  15. Example#6 • Graph the line described by the equation. • y + 3 = 0(x – 4)

  16. Solution to example#6 • Step 1 Plot (4, –3). • Step 2 There slope is 0. Every value of x will be at y = –3. • Step 3 Draw the line connecting the points.

  17. Student guided practice • Do problems 4-6 in your book page 279

  18. Exaxmple#7 • Write the equation that describes each line in slope-intercept form. • Slope = 3, (–1, 4) is on the line. • Solution: • Step 1 Write the equation in point-slope form: • y – y1 = m(x – x1) • y – 4 = 3[x – (–1)]

  19. Solution to Example#7 • Step 2 Write the equation in slope-intercept form by solving for y. • y – 4 = 3(x + 1). • y – 4 = 3x + 3Distribute 3 on the right side. + 4 + 4 Add 4 to both sides. y = 3x +7

  20. Example#8 • Write the equation that describes the line in slope-intercept form. • (2, –3) and (4, 1)

  21. Example#9 • Write the equation that describes the line in slope-intercept form.

  22. Student guided practice • Do problems 7-9 in your book page 279

  23. Finding intercepts • The points (1, –2) and (3, 10) are on a line . Find the intercepts.

  24. Example#10 • The points (2, 15) and (–4, –3) are on a line. Find the intercepts.

  25. Student guided practice • Do problems 13 and 14 in your book page 279.

  26. 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.

  27. solution

  28. Problem solving application • What if…? At a newspaper the costs to place an ad for one week are shown. Write an equation in slope-intercept form that represents this linear function. Then find the cost of an ad that is 21 lines long.

  29. solution

  30. Homework • Do evens problems from 23-33 pg. 280

  31. Closure • Today we learned how to write equations in slope intercept form. • Next class we are going to have a discovery activity to find the line of best fit.

  32. Have a great day

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