Question

writing equationsfrom graphs, two points, & tablesdirections: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 | 5 | 20 || y | 42 | 30 | 16 | 6 |m:b:equation:3.m:b:equation:4.| x | y || 51 | -50 || 39 | -34 || -15 | 38 || -21 | 46 |m:b:equation:

Explanation:

Step1: Calculate slope for (1)

Use 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 (1)

Substitute $(6,0)$ into $y=mx+b$
$0=-\frac{1}{2}(6)+b \implies 0=-3+b \implies b=3$

Step3: Write equation for (1)

Substitute $m$ and $b$ into $y=mx+b$
$y=-\frac{1}{2}x+3$
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Step4: Calculate slope for (2)

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

Step5: Find y-intercept for (2)

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

Step6: Write equation for (2)

Substitute $m$ and $b$ into $y=mx+b$
$y=-\frac{4}{5}x+22$
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Step7: Identify points for (3)

Graph has points $(-3,-1)$ and $(3,-1)$

Step8: Calculate slope for (3)

$m=\frac{-1-(-1)}{3-(-3)}=\frac{0}{6}=0$

Step9: Find y-intercept for (3)

Horizontal line at $y=-1$, so $b=-1$

Step10: Write equation for (3)

$y=-1$
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Step11: Calculate slope for (4)

Use two table points, e.g., $(51,-50)$ and $(39,-34)$
$m=\frac{-34-(-50)}{39-51}=\frac{16}{-12}=-\frac{4}{3}$

Step12: Find y-intercept for (4)

Substitute $(51,-50)$ into $y=mx+b$
$-50=-\frac{4}{3}(51)+b \implies -50=-68+b \implies b=18$

Step13: Write equation for (4)

Substitute $m$ and $b$ into $y=mx+b$
$y=-\frac{4}{3}x+18$

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.
$m$: $-\frac{4}{3}$
$b$: $18$
Equation: $y=-\frac{4}{3}x+18$