Question

writing equations
from graphs, two points, & tables
directions:
find the slope and the y-intercept of each representation.
then write a linear equation that would be represent the representation given.

1. (-22,14) and (6,0)

m: b:
equation:
2.

x	-25	-10	15	20
y	42	30	10	6

m: b:
equation:
3.
coordinate grid graph

m: b:
equation:
4.

x	31	39	-15	-21
y	-50	-34	38	46

m: b:
equation:

Explanation:

Step1: Calculate slope for Q1

Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{0-14}{6-(-22)}=\frac{-14}{28}=-\frac{1}{2}$

Step2: Find y-intercept for Q1

Substitute $(-22,14), m=-\frac{1}{2}$ into $y=mx+b$
$14 = -\frac{1}{2}(-22)+b \implies 14=11+b \implies b=3$

Step3: Write equation for Q1

Linear form: $y=mx+b$
$y=-\frac{1}{2}x+3$
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Step4: Calculate slope for Q2

Use two points $(-25,42), (-10,30)$
$m=\frac{30-42}{-10-(-25)}=\frac{-12}{15}=-\frac{4}{5}$

Step5: Find y-intercept for Q2

Substitute $(-10,30), m=-\frac{4}{5}$ into $y=mx+b$
$30 = -\frac{4}{5}(-10)+b \implies 30=8+b \implies b=22$

Step6: Write equation for Q2

$y=-\frac{4}{5}x+22$
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Step7: Identify points for Q3

Graph has points $(-4,-1), (4,-1)$ (horizontal line)

Step8: Calculate slope & intercept for Q3

Horizontal line slope: $m=0$; y-intercept $b=-1$

Step9: Write equation for Q3

$y=-1$
---

Step10: Calculate slope for Q4

Use two points $(31,-50), (39,-34)$
$m=\frac{-34-(-50)}{39-31}=\frac{16}{8}=2$

Step11: Find y-intercept for Q4

Substitute $(31,-50), m=2$ into $y=mx+b$
$-50=2(31)+b \implies -50=62+b \implies b=-112$

Step12: Write equation for Q4

$y=2x-112$

Answer:

1. $m: -\frac{1}{2}$, $b: 3$, Equation: $y=-\frac{1}{2}x+3$
2. $m: -\frac{4}{5}$, $b: 22$, Equation: $y=-\frac{4}{5}x+22$
3. $m: 0$, $b: -1$, Equation: $y=-1$
4. $m: 2$, $b: -112$, Equation: $y=2x-112$