Question

1. a. slope 2 and passing through (10, 17).

b. passing through (1, -4) and (-2, 5).
c.

x	-6	-3	0	3	6
y	-6	-4	-2	0	2

d. image of a line graph on a grid with x from 1 to 8 and y from 4 to 24

Explanation:

Part a

Step1: Use point-slope form

Point-slope formula: $y - y_1 = m(x - x_1)$ where $m=2$, $(x_1,y_1)=(10,17)$
$y - 17 = 2(x - 10)$

Step2: Simplify to slope-intercept form

Expand and isolate $y$:
$y - 17 = 2x - 20$
$y = 2x - 20 + 17$
$y = 2x - 3$

Part b

Step1: Calculate slope $m$

Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$ where $(x_1,y_1)=(1,-4)$, $(x_2,y_2)=(-2,5)$
$m=\frac{5 - (-4)}{-2 - 1}=\frac{9}{-3}=-3$

Step2: Use point-slope form

Substitute $m=-3$ and $(1,-4)$:
$y - (-4) = -3(x - 1)$

Step3: Simplify to slope-intercept form

$y + 4 = -3x + 3$
$y = -3x + 3 - 4$
$y = -3x - 1$

Part c

Step1: Calculate slope $m$

Use $(x_1,y_1)=(0,-2)$ and $(x_2,y_2)=(3,0)$:
$m=\frac{0 - (-2)}{3 - 0}=\frac{2}{3}$

Step2: Identify y-intercept $b$

When $x=0$, $y=-2$, so $b=-2$

Step3: Write slope-intercept equation

$y = \frac{2}{3}x - 2$

Part d

Step1: Identify y-intercept $b$

Line crosses y-axis at $(0,8)$, so $b=8$

Step2: Calculate slope $m$

Use $(x_1,y_1)=(0,8)$ and $(x_2,y_2)=(8,28)$:
$m=\frac{28 - 8}{8 - 0}=\frac{20}{8}=\frac{5}{2}$

Step3: Write slope-intercept equation

$y = \frac{5}{2}x + 8$

Answer:

a. $y = 2x - 3$
b. $y = -3x - 1$
c. $y = \frac{2}{3}x - 2$
d. $y = \frac{5}{2}x + 8$