Sure, let's tackle this step-by-step.
### Part A: Finding the x-intercept
1. The x-intercept of a line is the point where the graph intersects the x-axis. At this point, the value of y is always 0.
2. We start with the given linear equation:
[tex]\[
6x - 3y = 24
\][/tex]
3. To find the x-intercept, we substitute [tex]\( y = 0 \)[/tex] into the equation:
[tex]\[
6x - 3(0) = 24
\][/tex]
Simplifying, we get:
[tex]\[
6x = 24
\][/tex]
4. Solving for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{24}{6}
\][/tex]
[tex]\[
x = 4
\][/tex]
Therefore, the x-intercept is at the point [tex]\( (4, 0) \)[/tex].
### Part B: Interpreting the x-intercept in the context of the problem
The x-intercept [tex]\( (4, 0) \)[/tex] represents the time in minutes when Shari's distance from her home, [tex]\( y \)[/tex], is zero blocks—that is, when she is at her home.
So, the x-intercept tells us that Shari ran past her home after 4 minutes.
Thus:
- The point where the graph intersects the x-axis is [tex]\( (4, 0) \)[/tex].
- Shari ran past her home after 4 minutes.
