Question

1. graphing linear equations (graph - 10 points; y - intercept - 5 points; zero - 5 points) a linear function has an x - intercept of - 8 and a slope of $\frac{3}{4}$. the y - intercept of this function is __. zero of the function: __

Explanation:

Step1: Recall linear - function formula

The slope - intercept form of a linear function is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. We know the x - intercept is the point where $y = 0$, and the x - intercept is $x=-8$, and the slope $m=\frac{3}{4}$.

Step2: Substitute x - intercept values into the equation

When $y = 0$ and $x=-8$, we substitute into $y=mx + b$. So $0=\frac{3}{4}\times(-8)+b$.

Step3: Solve for b

First, calculate $\frac{3}{4}\times(-8)=-6$. Then the equation becomes $0=-6 + b$. Solving for $b$, we get $b = 6$.

Answer:

6