Question

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

x y

m: b:
equation:

12.
x 48 36 -4 -16
y 9 4 -6 -23

m: b:
equation:

13.

m: b:
equation:

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

x y

m: b:
equation:

15.
x y
12 -35
28 -23
36 -17
40 -14

m: b:
equation:

16.

m: b:
equation:

Explanation:

Problem 11: (-12,-2) and (6,4)

Step1: Calculate slope m

Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{4-(-2)}{6-(-12)}=\frac{6}{18}=\frac{1}{3}$

Step2: Find y-intercept b

Use $y=mx+b$ with $(6,4)$:
$4=\frac{1}{3}(6)+b \implies 4=2+b \implies b=2$

Step3: Write equation

$y=\frac{1}{3}x+2$

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Problem 12: Table of (48,9), (36,4), (-4,-6), (-16,-23)

Step1: Calculate slope m

Use $(48,9)$ and $(36,4)$:
$m=\frac{4-9}{36-48}=\frac{-5}{-12}=\frac{5}{12}$

Step2: Find y-intercept b

Use $y=mx+b$ with $(48,9)$:
$9=\frac{5}{12}(48)+b \implies 9=20+b \implies b=-11$

Step3: Write equation

$y=\frac{5}{12}x-11$

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Problem 13: Graph with points (1,3) and (5,1)

Step1: Calculate slope m

$m=\frac{1-3}{5-1}=\frac{-2}{4}=-\frac{1}{2}$

Step2: Find y-intercept b

Use $y=mx+b$ with $(1,3)$:
$3=-\frac{1}{2}(1)+b \implies b=3+\frac{1}{2}=\frac{7}{2}$

Step3: Write equation

$y=-\frac{1}{2}x+\frac{7}{2}$

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Problem 14: (33,-25) and (51,-37)

Step1: Calculate slope m

$m=\frac{-37-(-25)}{51-33}=\frac{-12}{18}=-\frac{2}{3}$

Step2: Find y-intercept b

Use $y=mx+b$ with $(33,-25)$:
$-25=-\frac{2}{3}(33)+b \implies -25=-22+b \implies b=-3$

Step3: Write equation

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

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Problem 15: Table of (12,-35), (28,-23), (36,-17), (40,-14)

Step1: Calculate slope m

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

Step2: Find y-intercept b

Use $y=mx+b$ with $(12,-35)$:
$-35=\frac{3}{4}(12)+b \implies -35=9+b \implies b=-44$

Step3: Write equation

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

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Problem 16: Vertical line at x=2

Step1: Identify slope and intercept

Vertical lines have undefined slope, no y-intercept.

Step2: Write equation

$x=2$

Answer:

1. $m=\frac{1}{3}$, $b=2$, Equation: $y=\frac{1}{3}x+2$
2. $m=\frac{5}{12}$, $b=-11$, Equation: $y=\frac{5}{12}x-11$
3. $m=-\frac{1}{2}$, $b=\frac{7}{2}$, Equation: $y=-\frac{1}{2}x+\frac{7}{2}$
4. $m=-\frac{2}{3}$, $b=-3$, Equation: $y=-\frac{2}{3}x-3$
5. $m=\frac{3}{4}$, $b=-44$, Equation: $y=\frac{3}{4}x-44$
6. $m=\text{undefined}$, $b=\text{none}$, Equation: $x=2$