Answered

The equation [tex]\( 6x - 3y = 24 \)[/tex] represents Shari's distance from home, [tex]\( y \)[/tex], in blocks, on her run across town over time, [tex]\( x \)[/tex], in minutes.

Part A:
At what point does the graph of the line intersect the [tex]\( x \)[/tex]-axis?
[tex]\[ (\square, \square) \][/tex]

Part B:
What does this point represent?
Shari ran past her home after [tex]\[ \square \][/tex] minutes.



Answer :

GinnyAnswer
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.

Other Questions