Question

y - intercept (0, 2) x - intercept (-4, 0) slope: equation: zero of the function: (-3, 0) (0, -2) (-4, 0) (0, 2) 2/3 3/2 y = 2/3x - 3 y = 3/2x + 2 y = 3/2x + 2 y = 3/2x - 3

Explanation:

Step1: Recall slope - formula

The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. We know two points on the line: the $y$-intercept $(0,2)$ and the $x$-intercept $(- 4,0)$. Let $(x_1,y_1)=(-4,0)$ and $(x_2,y_2)=(0,2)$. Then $m=\frac{2 - 0}{0-(-4)}=\frac{2}{4}=\frac{1}{2}$.

Step2: Recall slope - intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the $y$-intercept. We found $m=\frac{1}{2}$ and $b = 2$ (from the $y$-intercept $(0,2)$). So the equation of the line is $y=\frac{1}{2}x + 2$.

Step3: Recall zero of a function

The zero of a function is the $x$-value when $y = 0$. We know from the $x$-intercept that when $y = 0$, $x=-4$.

Answer:

slope: $\frac{1}{2}$
equation: $y=\frac{1}{2}x + 2$
zero of the function: $-4$