Chapter 6 Equations of a line

1. Determine the slope of this line segment. -4 6

2. Is the slope of this line segment positive, negative, zero, or not defined?

3. Determine the slope of a line that is perpendicular to the line through W(–9, 7) and X(6, –10). 4. For a service call, a plumber charges a $95 initial fee, plus $45 for each hour he works. Write an equation to represent the total cost, C dollars, for t hours of work. WX - Slope = C = 45t + 95

-5 1 5. Write an equation to describe this graph. y = mx + b -1 b = y = x – 1 -5 1 y – y1= m(x – x1) y – (-2)= (x – 5) y + 2 = (x – 5)

6. Describe the graph of the linear function with this equation: Slope = Point = (2, -3)

7. Which graph represents the equation a) c) b) d) m = p = (-3, -1)

8. Write this equation in slope-intercept form: First Method y = mx + b x5 x5

8. Write this equation in slope-intercept form: Second Method - 1/5 y – intercept: x5 x5

9. Determine the y-intercept of the graph of this equation: (0,23)

x1 y1 x2 y2 y – y1= m(x – x1) m = y – 4= (x + 2) or y – 6= (x + 9) 10. Write an equation in slope-point form for the line that passes through A(–2, 4) and B(–9, 6). x1 y1 x2 y2 y – y1= m(x – x1) m = y – 4= (x + 2) or y – 6= (x + 9)

y – 3= 7(x + 3) y – y1= m(x – x1) y – 3= 7x + 21 y – 3= 7(x + 3) 11. Write an equation for the line that passes through T(–3, 3) and is parallel to the line Parallel  m = 7 a) In point-slope form b) In slope-intercept form c) In general form y – 3= 7(x + 3) y – y1= m(x – x1) y – 3= 7x + 21 y – 3= 7(x + 3) y = 7x + 21 +3 y = 7x + 24 y = 7x + 24 – y – y 0 = 7x – y + 24 7x – y + 24 = 0

12. Write this equation in general form: 3( )

13. Determine the slope of the line with this equation: -7x -7x -5 -5 3 3 3

14. The coordinates of the endpoints of segments are given below 14. The coordinates of the endpoints of segments are given below. State whether they are parallel, perpendicular, or neither? R(–2, 8), S(–12, –4) and T(3, –1), U(9, 4) mRS = mTU = Neither

15. Determine the x- and y-intercepts of the graph of this equation: 5x +8y + 40 = 0 x-intercept  y = y-intercept  x = 5(0) + 8y + 40 = 0 5x + 8(0) + 40 = 0 5x + 40 = 0 8y + 40 = 0 -40 -40 -40 -40 5x = -40 8y = -40 8 8 5 5 x = -8 y = -5

y – y1= m(x – x1) y – 5= (x + 2) y – 5= (x + 2) 16. Write an equation, in slope-point form, for the line that passes through B(–2, 5) and is: a) parallel to the line b) perpendicular to the line y – y1= m(x – x1) (x + 2) y – 5= (x + 2) y – 5=