Question

watch the video and then solve the problem given below.
click here to watch the video.
use the graph to determine the following.
a. the x-intercepts, if any
b. the y-intercept, if any
choice
a. x = -4
b. there is no x-intercept.
b. what is the y-intercept? select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. y =
b. there is no y-intercept.

Explanation:

Step1: Identify x-intercept

The x-intercept is where the line crosses the x-axis ($y=0$). From the graph, this occurs at $x=-4$.

Step2: Identify y-intercept

The y-intercept is where the line crosses the y-axis ($x=0$). To find it, first determine the line's equation. The line passes through $(-4,0)$ and $(3,6)$. Calculate slope:
$\text{slope } m = \frac{6-0}{3-(-4)} = \frac{6}{7}$
Use point-slope form $y - y_1 = m(x - x_1)$ with $(-4,0)$:
$y - 0 = \frac{6}{7}(x + 4)$
Substitute $x=0$ to find y-intercept:
$y = \frac{6}{7}(0 + 4) = \frac{24}{7} \approx 3.43$, or directly observe the line crosses the y-axis at $y=\frac{24}{7}$.

Answer:

a. A. $x = -4$
b. A. $y=\frac{24}{7}$