1-4 and 1-5Writing Linear Equations and Writing Equations of Parallel and

Perpendicular Lines

Equations of lines:

Standard form: Ax + By = C

Slope-intercept form: y = mx + b

Point-slope form: y - y1 = m(x - x1)

How to tell if lines are parallel or perpendicular:

Parallel lines have the same slope

Perpendicular lines have slopes that are opposite reciprocals

coincide: two lines that are the same

examples:

1. Write an equation in slope-intercept from.

a) m = -3/4 y-intercept = 7 b) m = -6 and passes thru (1,-3)

c) m = 1/2 y- intercept = 4 d) m = 2 and passes thru (-3,2)

e) passes thru (5,6) and (-1,2) f) vertical and passes thru (8,9)

2. Mrs. Alvarez is preparing her art classroom for a new year of school. She placed a purchase order for $800 to buy paper, chalk, and clay. In addition, she expects the expenses each month to be $120. Write an equation that models the total expense y after x months.

3. Alvin Hawkins is opening a home-based business. He determined that he will need $6000 to buy a computer and supplies to start. He expects expenses for each following month to be $700. Write an equation that models the total expense y after x months.

4.

5. Over time, the percent of registered voters turning out to vote in the United states has been declining. The table shows the percent of registered voters who voted in presidential elections from 1964 to 1996.

elections since total voter turnout1964 (% of registered

voters)

0 95.81 89.72 79.93 77.64 76.55 74.66 72.57 78.28 63.4

a)find a linear equation that can be used as a model to predict the average percent of registered-voter turnout for any US presidential election.

b) assume that the rate of decrease of voter turnout remains constant over time and use the equations to predict voter turnout ins the year 2008.

c) evaluate the prediction.

6. Determine whether the graphs of each pair of equations are parallel, coinciding, or neither.

a) 3x - 4y = 12 and 9x - 12y = 72

b) 15x + 12y = 36 and 5x + 4y = 12

c) 2x + 4y = 4 and x + 2y = 5

d) 5x - 3y = 12 and 10x - 6y = 24

7.

8. Mrs. Lewis worked the concession stand at the football game for two consecutive Friday nights. On the first Friday night she sold 520 hotdogs and 280 cups of soda. On the second Friday night, she sold 390 hotdogs and 210 cups of soda. Could the sales on the second Friday have totaled $1057.50 if her sales on the first Friday were $1410. Explain.

9. Write the standard form of the equation of the line that passes through the point at (4,-7) and is parallel to the graph of 2x -5y + 8 = 0.

10. Write the standard form of the equation of the line that passes through the point (-2,10) and is parallel to the graph of 2x + 5y + 4 = 0.

11. Write the standard form of the equation of the line that passes through the point at (-6,-1) and is perpendicular to the graph of 4x +3y -7 = 0.

12. Write the standard form of the equation of the line that passes through the point (2,-3) and is perpendicular to the graph of 6x - 8y - 5 = 0.

13. Determine the equation of the perpendicular bisector of the line segment with endpoints S(3,4) and T(11,18).

14. Determine the equation of the perpendicular bisector of the line segment with endpoints A(2,3) and B(6,-1).