Question

1. what is the equation of a line that passes through the points (-3, -2) and (1, 2)?

Explanation:

Step1: Calculate the slope

The slope formula is $m=\frac{y_2-y_1}{x_2-x_1}$. Substitute $(x_1,y_1)=(-3,-2)$ and $(x_2,y_2)=(1,2)$:
$m=\frac{2-(-2)}{1-(-3)}=\frac{4}{4}=1$

Step2: Find y-intercept $b$

Use slope-intercept form $y=mx+b$, substitute $m=1$ and $(x,y)=(1,2)$:
$2=1\times1+b$
Solve for $b$: $b=2-1=1$

Step3: Write line equation

Substitute $m=1$ and $b=1$ into $y=mx+b$:
$y=x+1$

Answer:

$y=x+1$