Question

name: _____ period__
find the slope, y-intercept of the line, and then write an equation in slope-intercept form.
1)
points: (2,4), (5,0)
m: _______
b: _______
equation: _______
2)
points: (-5,-1), (-1,-4)
m: _______
b: _______
equation: _______
3)
points: (-3,3), (0,3)
m: _______
b: _______
equation: _______
4)
points: (0,1), (2,-2)
m: _______
b: _______
equation: _______
5)
points: (-5,5), (-3,3)
m: _______
b: _______
equation: _______
6)
points: (-4,-1), (-2,-2)
m: _______
b: _______
equation: _______

Explanation:

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Problem 1

Step1: Identify two points

Points: $(2,4)$ and $(5,0)$

Step2: Calculate slope $m$

Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{0-4}{5-2}=-\frac{4}{3}$

Step3: Find y-intercept $b$

Substitute $(5,0)$ into $y=mx+b$:
$0=-\frac{4}{3}(5)+b$
$b=\frac{20}{3}$

Step4: Write slope-intercept equation

$y=mx+b$
$y=-\frac{4}{3}x+\frac{20}{3}$

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Problem 2

Step1: Identify two points

Points: $(-5,-1)$ and $(-1,-4)$

Step2: Calculate slope $m$

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

Step3: Find y-intercept $b$

Substitute $(-5,-1)$ into $y=mx+b$:
$-1=-\frac{3}{4}(-5)+b$
$-1=\frac{15}{4}+b$
$b=-1-\frac{15}{4}=-\frac{19}{4}$

Step4: Write slope-intercept equation

$y=-\frac{3}{4}x-\frac{19}{4}$

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Problem 3

Step1: Identify two points

Points: $(-3,3)$ and $(0,3)$

Step2: Calculate slope $m$

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

Step3: Find y-intercept $b$

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

Step4: Write slope-intercept equation

$y=0x+3$
$y=3$

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Problem 4

Step1: Identify two points

Points: $(0,1)$ and $(2,-2)$

Step2: Calculate slope $m$

$m=\frac{-2-1}{2-0}=\frac{-3}{2}=-\frac{3}{2}$

Step3: Find y-intercept $b$

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

Step4: Write slope-intercept equation

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

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Problem 5

Step1: Identify two points

Points: $(-5,5)$ and $(-1,3)$

Step2: Calculate slope $m$

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

Step3: Find y-intercept $b$

Substitute $(-1,3)$ into $y=mx+b$:
$3=-\frac{1}{2}(-1)+b$
$3=\frac{1}{2}+b$
$b=3-\frac{1}{2}=\frac{5}{2}$

Step4: Write slope-intercept equation

$y=-\frac{1}{2}x+\frac{5}{2}$

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Problem 6

Step1: Identify two points

Points: $(-4,3)$ and $(-2,2)$

Step2: Calculate slope $m$

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

Step3: Find y-intercept $b$

Substitute $(-2,2)$ into $y=mx+b$:
$2=-\frac{1}{2}(-2)+b$
$2=1+b$
$b=1$

Step4: Write slope-intercept equation

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

Answer:

1. $m=-\frac{4}{3}$, $b=\frac{20}{3}$, Equation: $y=-\frac{4}{3}x+\frac{20}{3}$
2. $m=-\frac{3}{4}$, $b=-\frac{19}{4}$, Equation: $y=-\frac{3}{4}x-\frac{19}{4}$
3. $m=0$, $b=3$, Equation: $y=3$
4. $m=-\frac{3}{2}$, $b=1$, Equation: $y=-\frac{3}{2}x+1$
5. $m=-\frac{1}{2}$, $b=\frac{5}{2}$, Equation: $y=-\frac{1}{2}x+\frac{5}{2}$
6. $m=-\frac{1}{2}$, $b=1$, Equation: $y=-\frac{1}{2}x+1$