Question

1. (-8, 6) and (-2, 9); m = ____ b=____

equation= _______________

1. (-1, -1) and (1, 5); m = ____,b=__

equation= _______________

1. (2, 4) and (3, 6); m = 2 b= 0

$\frac{y_1 + y_2}{x_1 + x_2} = \frac{6 + 4}{3+2}=\frac{10}{5}$ or 2

1. (-2, 3) and (2, 7); m = 1

$m=\frac{7 + 3}{2+2}=\frac{4}{4}$
$y=mx+b$

Explanation:

Step1: Calculate slope for 7)

Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{9-6}{-2-(-8)}=\frac{3}{6}=\frac{1}{2}$

Step2: Find y-intercept for 7)

Use $y=mx+b$, plug $(-8,6)$:
$6=\frac{1}{2}(-8)+b$
$6=-4+b$
$b=10$

Step3: Write equation for 7)

Substitute $m$ and $b$:
$y=\frac{1}{2}x+10$

Step4: Calculate slope for 8)

Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{5-(-1)}{1-(-1)}=\frac{6}{2}=3$

Step5: Find y-intercept for 8)

Use $y=mx+b$, plug $(-1,-1)$:
$-1=3(-1)+b$
$-1=-3+b$
$b=2$

Step6: Write equation for 8)

Substitute $m$ and $b$:
$y=3x+2$

Step7: Verify slope for 11)

Slope formula: $m=\frac{6-4}{3-2}=\frac{2}{1}=2$

Step8: Verify y-intercept for 11)

Use $y=mx+b$, plug $(2,4)$:
$4=2(2)+b$
$4=4+b$
$b=0$

Step9: Write equation for 11)

Substitute $m$ and $b$:
$y=2x$

Step10: Calculate slope for 12)

Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{7-3}{2-(-2)}=\frac{4}{4}=1$

Step11: Find y-intercept for 12)

Use $y=mx+b$, plug $(-2,3)$:
$3=1(-2)+b$
$3=-2+b$
$b=5$

Step12: Write equation for 12)

Substitute $m$ and $b$:
$y=x+5$

Answer:

1. $m=\frac{1}{2}$, $b=10$, Equation: $y=\frac{1}{2}x+10$
2. $m=3$, $b=2$, Equation: $y=3x+2$
3. $m=2$, $b=0$, Equation: $y=2x$
4. $m=1$, $b=5$, Equation: $y=x+5$