Question

what is the equation of this line? options: y = -x + 2, cannot be determined, y = 2x - 2, y = 2x + 2

Explanation:

Step1: Identify two points on line

Take points $(-3, 5)$ and $(-2, 4)$ (from the graph)

Step2: Calculate slope $m$

Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{4-5}{-2-(-3)}=\frac{-1}{1}=-1$

Step3: Find y-intercept $b$

Use point $(-2,4)$ in $y=mx+b$:
$4 = -1\times(-2)+b$
$4=2+b$
$b=4-2=2$

Step4: Write line equation

Substitute $m=-1, b=2$ into $y=mx+b$

Answer:

A. $y = -x + 2$