To understand the graph of the given relationship [tex]\( 4x + 6y = 36 \)[/tex], we need to find the intercepts where the line crosses the x-axis and the y-axis.
### Finding the Intercepts:
1. x-intercept (where the line crosses the x-axis):
- Set [tex]\( y = 0 \)[/tex] in the equation [tex]\( 4x + 6y = 36 \)[/tex].
- The equation becomes [tex]\( 4x = 36 \)[/tex].
- Solving for [tex]\( x \)[/tex], we get:
[tex]\[
x = \frac{36}{4} = 9
\][/tex]
- So the x-intercept is [tex]\( (9, 0) \)[/tex].
2. y-intercept (where the line crosses the y-axis):
- Set [tex]\( x = 0 \)[/tex] in the equation [tex]\( 4x + 6y = 36 \)[/tex].
- The equation becomes [tex]\( 6y = 36 \)[/tex].
- Solving for [tex]\( y \)[/tex], we get:
[tex]\[
y = \frac{36}{6} = 6
\][/tex]
- So the y-intercept is [tex]\( (0, 6) \)[/tex].
### Conclusion:
The line represented by the equation [tex]\( 4x + 6y = 36 \)[/tex] passes through the points [tex]\( (9, 0) \)[/tex] and [tex]\( (0, 6) \)[/tex].
Given the above intercepts, we can now match this with the provided options:
- A. The graph is a line that goes through the points [tex]\( (9, 0) \)[/tex] and [tex]\( (0, 6) \)[/tex].
Thus, the correct answer is:
A. The graph is a line that goes through the points [tex]\( (9, 0) \)[/tex] and [tex]\( (0, 6) \)[/tex].
