Question

5)
(-5,5)
(-1,3)
| x | y
|-5|5
|-1|3
m: ______
b: ______
equation: ______
6)
(-4,3)
(-2,2)
| x | y
|-4|3
|-2|2
m: ______
b: ______
equation: ______

Explanation:

For problem 5:

Step1: Calculate slope $m$

Use slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
Points $(-5,5)$ and $(-1,3)$:
$m=\frac{3-5}{-1-(-5)}=\frac{-2}{4}=-\frac{1}{2}$

Step2: Solve for y-intercept $b$

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

Step3: Write linear equation

Use $y=mx+b$:
$y = -\frac{1}{2}x + \frac{5}{2}$

Step1: Calculate slope $m$

Use slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
Points $(-4,-1)$ and $(-2,-2)$:
$m=\frac{-2-(-1)}{-2-(-4)}=\frac{-1}{2}=-\frac{1}{2}$

Step2: Solve for y-intercept $b$

Substitute $m=-\frac{1}{2}$ and $(-4,-1)$ into $y=mx+b$:
$-1 = -\frac{1}{2}(-4) + b$
$-1 = 2 + b$
$b = -1 - 2 = -3$

Step3: Write linear equation

Use $y=mx+b$:
$y = -\frac{1}{2}x - 3$

Answer:

$m=-\frac{1}{2}$, $b=\frac{5}{2}$, Equation: $y=-\frac{1}{2}x+\frac{5}{2}$

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For problem 6: