# Solutions 9: Graphs of Linear Functions

## Solutions to Try Its

1.

$\left(-3,7\right)$
,
$\left(-6,9\right)$
, or
$\left(-9,11\right)$
.

3.

4.
$\left(16,\text{ 0}\right)$

5. a.
$f\left(x\right)=2x$

b.
$g\left(x\right)=-\frac{1}{2}x$

6.
$y=-\frac{1}{3}x+6$

7.

a.

$\left(0,5\right)$

b.

$\left(5,\text{ 0}\right)$

c. Slope -1

d. Neither parallel nor perpendicular

e. Decreasing function

f. Given the identity function, perform a vertical flip (over the t-axis) and shift up 5 units.

## Solutions to Odd-Numbered Exercises

1. The slopes are equal; y-intercepts are not equal.

3. The point of intersection is
$\left(a,a\right)$
. This is because for the horizontal line, all of the y coordinates are a and for the vertical line, all of the x coordinates are a. The point of intersection will have these two characteristics.

5. First, find the slope of the linear function. Then take the negative reciprocal of the slope; this is the slope of the perpendicular line. Substitute the slope of the perpendicular line and the coordinate of the given point into the equation
$y=mx+b$
and solve for b. Then write the equation of the line in the form
$y=mx+b$
by substituting in m and b.

7. neither parallel or perpendicular

9. perpendicular

11. parallel

13.
$\left(-2\text{, }0\right)$
;
$\left(0\text{, 4}\right)$

15.
$\left(\frac{1}{5}\text{, }0\right)$
;
$\left(0\text{, 1}\right)$

17.
$\left(8\text{, }0\right)$
;
$\left(0\text{, }28\right)$

19.
$\text{Line 1}: m=8 \text{ Line 2}: m=-6 \text{Neither}$

21.
$\text{Line 1}: m=-\frac{1}{2} \text{ Line 2}: m=2 \text{Perpendicular}$

23.
$\text{Line 1}: m=-2 \text{ Line 2}: m=-2 \text{Parallel}$

25.
$g\left(x\right)=3x - 3$

27.
$p\left(t\right)=-\frac{1}{3}t+2$

29.
$\left(-2,1\right)$

31.
$\left(-\frac{17}{5},\frac{5}{3}\right)$

33. F

35. C

37. A

39.

41.

43.

45.

47.

49.

51.

53.

55.

57.

59.
$g\left(x\right)=0.75x - 5.5\text{}$
0.75
$\left(0,-5.5\right)$

61.
$y=3$

63.
$x=-3$

65. no point of intersection

67.
$\left(\text{2},\text{ 7}\right)$

69.
$\left(-10,\text{ }-5\right)$

71.
$y=100x - 98$

73.
$x<\frac{1999}{201}x>\frac{1999}{201}$

75. Less than 3000 texts