write an equation for the line in slope - intercept form. (use integers or fractions for any numbers in the…

Explanation:

Step1: Identify the y - intercept

The line crosses the y - axis at the point $(0,2)$, so $b = 2$.

Step2: Calculate the slope

Pick two points on the line, say $(0,2)$ and $(- 2,-2)$. The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Then $m=\frac{-2 - 2}{-2-0}=\frac{-4}{-2}=2$.

Step3: Write the equation in slope - intercept form

The slope - intercept form of a line is $y=mx + b$. Substituting $m = 2$ and $b = 2$ gives $y=2x + 2$.

Answer:

$y = 2x+2$