Question

42 the graph of linear function g is shown on the grid. what is the zero of g? record your answer and fill in the bubbles on your answer document.

Explanation:

Step1: Find the slope formula

The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(-8,3)$ and $(x_2,y_2)=(-3,-4.5)$. Then $m=\frac{-4.5 - 3}{-3-(-8)}=\frac{-7.5}{5}=-1.5$.

Step2: Use the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$. Using the point $(-8,3)$ and $m=-1.5$, we have $y - 3=-1.5(x + 8)$.

Step3: Simplify the equation

Expand the right - hand side: $y-3=-1.5x-12$. Then $y=-1.5x - 9$.

Step4: Find the zero

The zero of the function is the $x$ - value when $y = 0$. Set $y = 0$ in the equation $0=-1.5x - 9$. Add $1.5x$ to both sides: $1.5x=-9$. Divide both sides by $1.5$: $x=-6$.

Answer:

$-6$