Question

1. (-12,-2) and (6,4)

x y
m:
b:
equation:
12.
x 48 36 -4 -8
y 9 4 -6 -23
m:
b:
equation:
13.
graph of a line on coordinate grid
m:
b:
equation:

1. (33,-25) and (51,-37)

x y
m:
b:
equation:
15.
x 12 28 36 40
y -35 -23 -17 -14
m:
b:
equation:
16.
graph of a vertical line on coordinate grid
m:
b:
equation:

Explanation:

Step1: Find slope for Q13

Identify points (0,2) and (4,0).
Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}=\frac{0-2}{4-0}=-\frac{1}{2}$

Step2: Find y-intercept for Q13

Graph crosses y-axis at (0,2), so $b=2$.

Step3: Write equation for Q13

Slope-intercept form: $y=mx+b$
$y=-\frac{1}{2}x+2$

Step4: Find slope for Q14

Use points (33,-25) and (51,-37).
$m=\frac{-37-(-25)}{51-33}=\frac{-12}{18}=-\frac{2}{3}$

Step5: Find y-intercept for Q14

Substitute $x=33,y=-25,m=-\frac{2}{3}$ into $y=mx+b$:
$-25=-\frac{2}{3}(33)+b$
$-25=-22+b$
$b=-25+22=-3$

Step6: Write equation for Q14

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

Step7: Find slope for Q15

Use points (12,-35) and (28,-23).
$m=\frac{-23-(-35)}{28-12}=\frac{12}{16}=\frac{3}{4}$

Step8: Find y-intercept for Q15

Substitute $x=12,y=-35,m=\frac{3}{4}$ into $y=mx+b$:
$-35=\frac{3}{4}(12)+b$
$-35=9+b$
$b=-35-9=-44$

Step9: Write equation for Q15

$y=\frac{3}{4}x-44$

Step10: Find slope for Q16

Vertical line has undefined slope.

Step11: Find intercept for Q16

Line is $x=2$, no y-intercept (b: none).

Step12: Write equation for Q16

$x=2$

Answer:

Question 13:

$m: -\frac{1}{2}$, $b: 2$, Equation: $y=-\frac{1}{2}x+2$

Question 14:

$m: -\frac{2}{3}$, $b: -3$, Equation: $y=-\frac{2}{3}x-3$

Question 15:

$m: \frac{3}{4}$, $b: -44$, Equation: $y=\frac{3}{4}x-44$

Question 16:

$m: \text{undefined}$, $b: \text{none}$, Equation: $x=2$