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 the slope - intercept form

The equation of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. The x - intercept is the value of $x$ when $y = 0$. Given $m=\frac{3}{4}$ and the x - intercept $x=-8,y = 0$.

Step2: Substitute values into the equation

Substitute $x=-8,y = 0$ and $m=\frac{3}{4}$ into $y=mx + b$. We get $0=\frac{3}{4}\times(-8)+b$.

Step3: Solve for $b$

First, calculate $\frac{3}{4}\times(-8)=-6$. Then the equation becomes $0=-6 + b$. Add 6 to both sides of the equation: $b = 6$.

Answer:

6