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# 3.5 write and graph equations of lines

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### 3.5 write and graph equations of lines

1. 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. 2. 3.5
3. 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. 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. 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. 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. 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. 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. 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. 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. 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. 12. 3.5
13. 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. 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. 15. 3.5Guided Practice 6. 2x – 3y = 6 Graph the equation. ANSWER
16. 16. 3.5Guided Practice Graph the equation. 7. y = 4 ANSWER
17. 17. 3.5Guided Practice Graph the equation. 8. x = – 3 ANSWER
18. 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. 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. 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. 21. 3.5 Homework Pg 190-193 #5, 20, 26, 39, 63