Question

#19-27, write the slope & y-intercept, then write the equation.
19.

m=____, b=____
eq: ______________
20.

m=____, b=____
eq: ______________
21.

m=____, b=____
eq: ______________
22.

m=____, b=____
eq: ______________
23.

m=____, b=____
eq: ______________
24.

m=____, b=____
eq: ______________
25.

m=____, b=____
eq: ______________
26.

m=____, b=____
eq: ______________
27.

m=____, b=____
eq: ______________

Explanation:

We use the slope-intercept form $y = mx + b$, where $m=\frac{\text{rise}}{\text{run}}$ is the slope, and $b$ is the y-intercept (where the line crosses the y-axis).

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Problem 19

Step1: Calculate slope

Points: $(0,3)$ and $(4,1)$
$m=\frac{1-3}{4-0}=\frac{-2}{4}=-\frac{1}{2}$

Step2: Identify y-intercept

Line crosses y-axis at $(0,3)$, so $b=3$

Step3: Write equation

Substitute $m$ and $b$ into $y=mx+b$
$y=-\frac{1}{2}x+3$

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Problem 20

Step1: Calculate slope

Points: $(-2,-2)$ and $(0,2)$
$m=\frac{2-(-2)}{0-(-2)}=\frac{4}{2}=2$

Step2: Identify y-intercept

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

Step3: Write equation

Substitute $m$ and $b$ into $y=mx+b$
$y=2x+2$

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Problem 21

Step1: Calculate slope

Points: $(0,1)$ and $(4,0)$
$m=\frac{0-1}{4-0}=-\frac{1}{4}$

Step2: Identify y-intercept

Line crosses y-axis at $(0,1)$, so $b=1$

Step3: Write equation

Substitute $m$ and $b$ into $y=mx+b$
$y=-\frac{1}{4}x+1$

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Problem 22

Step1: Calculate slope

Horizontal line: rise=0, so $m=0$

Step2: Identify y-intercept

Line crosses y-axis at $(0,-1)$, so $b=-1$

Step3: Write equation

Substitute $m$ and $b$ into $y=mx+b$
$y=-1$

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Problem 23

Step1: Calculate slope

Points: $(-2,-2)$ and $(1,1)$
$m=\frac{1-(-2)}{1-(-2)}=\frac{3}{3}=1$

Step2: Identify y-intercept

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

Step3: Write equation

Substitute $m$ and $b$ into $y=mx+b$
$y=x$

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Problem 24

Step1: Calculate slope

Points: $(0,0)$ and $(4,-1)$
$m=\frac{-1-0}{4-0}=-\frac{1}{4}$

Step2: Identify y-intercept

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

Step3: Write equation

Substitute $m$ and $b$ into $y=mx+b$
$y=-\frac{1}{4}x$

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Problem 25

Step1: Calculate slope

Points: $(0,-2)$ and $(4,-3)$
$m=\frac{-3-(-2)}{4-0}=\frac{-1}{4}=-\frac{1}{4}$

Step2: Identify y-intercept

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

Step3: Write equation

Substitute $m$ and $b$ into $y=mx+b$
$y=-\frac{1}{4}x-2$

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Problem 26

Step1: Calculate slope

Horizontal line: rise=0, so $m=0$

Step2: Identify y-intercept

Line crosses y-axis at $(0,-3)$, so $b=-3$

Step3: Write equation

Substitute $m$ and $b$ into $y=mx+b$
$y=-3$

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Problem 27

Step1: Calculate slope

Points: $(-2,3)$ and $(2,1)$
$m=\frac{1-3}{2-(-2)}=\frac{-2}{4}=-\frac{1}{2}$

Step2: Identify y-intercept

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

Step3: Write equation

Substitute $m$ and $b$ into $y=mx+b$
$y=-\frac{1}{2}x+2$

Answer:

Problem	$m$	$b$	Equation
20	$2$	$2$	$y=2x+2$
21	$-\frac{1}{4}$	$1$	$y=-\frac{1}{4}x+1$
22	$0$	$-1$	$y=-1$
23	$1$	$0$	$y=x$
24	$-\frac{1}{4}$	$0$	$y=-\frac{1}{4}x$
25	$-\frac{1}{4}$	$-2$	$y=-\frac{1}{4}x-2$
26	$0$	$-3$	$y=-3$
27	$-\frac{1}{2}$	$2$	$y=-\frac{1}{2}x+2$