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3.5 write and graph equations of lines
3.5 write and graph equations of lines
3.5 write and graph equations of lines
3.5 write and graph equations of lines
3.5 write and graph equations of lines
3.5 write and graph equations of lines
3.5 write and graph equations of lines
3.5 write and graph equations of lines
3.5 write and graph equations of lines
3.5 write and graph equations of lines
3.5 write and graph equations of lines
3.5 write and graph equations of lines
3.5 write and graph equations of lines
3.5 write and graph equations of lines
3.5 write and graph equations of lines
3.5 write and graph equations of lines
3.5 write and graph equations of lines
3.5 write and graph equations of lines
3.5 write and graph equations of lines
3.5 write and graph equations of lines
3.5 write and graph equations of lines
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3.5 write and graph equations of lines

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  • 1. 3.53.5 Write and Graph Equations of Lines Bell Thinger 1. If 2x + 5y = –20 and x = 0, what is y? ANSWER –4 2. What is the slope of the line containing the points (2, 7) and (3, –10)? ANSWER –17 3. Orphelia bought x apples. If each apple costs $.59, write an equation for y, the total cost of x apples. ANSWER y = 0.59x
  • 2. 3.5
  • 3. 3.5Example 1 SOLUTION m 4 – (– 2) 0 – 3 = 6 – 3= = – 2 STEP 2 Find the y-intercept. The line intersects the y-axis at the point (0, 4), so the y-intercept is 4. STEP 1 Find the slope. Choose two points on the graph of the line, (0, 4) and (3, –2). Write an equation of the line in slope- intercept form. STEP 3 Write the equation. y = –2x + 4 mx + by = Use slope-intercept form. Substitute – 2 for m and 4 for b.
  • 4. 3.5Example 2 Write an equation of the line passing through the point (– 1, 1) that is parallel to the line with the equation y = 2x – 3. SOLUTION STEP 1 Find the slope m. The slope of a line parallel to y = 2x –3 is the same as the given line, so the slope is 2. STEP 2 Find the y-intercept b by using m = 2 and (x, y) = (– 1, 1). y mx + b= 1 = 2 (–1 ) + b 3 = b Use slope-intercept form. Substitute for x, y, and m. Solve for b. Because m = 2 and b = 3, an equation of the line is y = 2x + 3.
  • 5. 3.5Example 3 Write an equation of the line j passing through the point (2, 3) that is perpendicular to the line k with the equation y = – 2x + 2. SOLUTION STEP 1 Find the slope m of line j. Line k has a slope of – 2. 1 2 m = The product of the slopes of lines is – 1. Divide each side by – 2. mx + by = 3 = 1 2 ( 2 ) + b 2 = b Use slope-intercept form. Substitute for x, y, and m. Solve for b. STEP 2 Find the y-intercept b by using m = and (x, y) = (2, 3). 1 2 – 2 m = – 1
  • 6. 3.5Example 3 Because m = and b = 2, an equation of line j is y = x + 2. You can check that the lines j and k are perpendicular by graphing, then using a protractor to measure one of the angles formed by the lines. 2 1 2 1
  • 7. 3.5Guided Practice Write an equation of the line in the graph at the right. 1. y = – 1 2 3 xANSWER Write an equation of the line that passes through (– 2, 5) and (1, 2). 2. ANSWER y = –x + 3
  • 8. 3.5Guided Practice Write an equation of the line that passes through the point (1, 5) and is parallel to the line with the equation 6x – 2y = 10. Graph the lines to check that they are parallel. 3. ANSWER y = 3x + 2
  • 9. 3.5Guided Practice How do you know the lines x = 4 and y = 2 are perpendicular? 4. x = 4 is a vertical line while y = 2 is a horizontal line. SAMPLE ANSWER
  • 10. 3.5Example 4 Gym Membership The graph models the total cost of joining a gym. Write an equation of the line. Explain the meaning of the slope and the y-intercept of the line. SOLUTION Find the slope.STEP 1 = 44m = 363 – 231 5 – 2 132 3 =
  • 11. 3.5Example 4 STEP 2 Find the y-intercept. Use the slope and one of the points on the graph. mx + by = 143 = b Use slope-intercept form. Substitute for x, y, and m. Simplify. STEP 3 Write the equation. Because m = 44 and b = 143, an equation of the line is y = 44x + 143. The equation y = 44x + 143 models the cost. The slope is the monthly fee, $44, and the y-intercept is the initial cost to join the gym, $143. 44 2 + b231 =
  • 12. 3.5
  • 13. 3.5Example 5 Graph 3x + 4y = 12. SOLUTION The equation is in standard form, so you can use the intercepts. STEP 1 Find the intercepts. To find the x-intercept, let y = 0. 3x + 4y = 12 3x +4 ( 0 ) = 12 x = 4 To find the y-intercept, let x = 0. 3x + 4y = 12 3 ( 0 ) + 4y = 12 y = 3
  • 14. 3.5Example 5 STEP 2 Graph the line. The intercepts are (4, 0) and (0, 3). Graph these points, then draw a line through the points.
  • 15. 3.5Guided Practice 6. 2x – 3y = 6 Graph the equation. ANSWER
  • 16. 3.5Guided Practice Graph the equation. 7. y = 4 ANSWER
  • 17. 3.5Guided Practice Graph the equation. 8. x = – 3 ANSWER
  • 18. 3.5Example 6 SOLUTION STEP 1 Model each rental with an equation. Cost of one month’s rental online: y = 15 Cost of one month’s rental locally: y = 4x, where x represents the number of DVDs rented DVD Rental You can rent DVDs at a local store for $4.00 each. An Internet company offers a flat fee of $15.00 per month for as many rentals as you want. How many DVDs do you need to rent to make the online rental a better buy?
  • 19. 3.5Example 6 Graph each equation.STEP 2 The point of intersection is (3.75, 15). Using the graph, you can see that it is cheaper to rent locally if you rent 3 or fewer DVDs per month. If you rent 4 or more DVDs per month, it is cheaper to rent online.
  • 20. 3.5Exit Slip y = x – 1ANSWER 4 3 2. Write an equation of the line that passes through the point (4, –2) and has slope 3. y = 3x – 14ANSWER 3. Write an equation of the line that passes through the point (7, 1) and is parallel to the line with equation x = 4. x = 7ANSWER 1. Write an equation of line that has slope and y-intercept – 1. 4 3 4. Write an equation of the line that passes through the point (7, 1) and is perpendicular to the line with equation 6x – 3y = 8. y = – x +ANSWER 2 1 2 9
  • 21. 3.5 Homework Pg 190-193 #5, 20, 26, 39, 63

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