Let's consider the given equation:
[tex]\[ 3x + 4y = 240 \][/tex]
To determine which statement is true about the graph of this equation, we will find the x-intercept and the y-intercept.
#### Step-by-Step Solution:
1. Finding the x-intercept:
- The x-intercept occurs when [tex]\( y = 0 \)[/tex].
- Substituting [tex]\( y = 0 \)[/tex] into the equation:
[tex]\[ 3x + 4(0) = 240 \][/tex]
[tex]\[ 3x = 240 \][/tex]
[tex]\[ x = \frac{240}{3} = 80 \][/tex]
- So the x-intercept is [tex]\((80, 0)\)[/tex].
2. Finding the y-intercept:
- The y-intercept occurs when [tex]\( x = 0 \)[/tex].
- Substituting [tex]\( x = 0 \)[/tex] into the equation:
[tex]\[ 3(0) + 4y = 240 \][/tex]
[tex]\[ 4y = 240 \][/tex]
[tex]\[ y = \frac{240}{4} = 60 \][/tex]
- So the y-intercept is [tex]\((0, 60)\)[/tex].
3. Conclusion:
- The graph of the equation [tex]\( 3x + 4y = 240 \)[/tex] is a line that goes through the points [tex]\((80, 0)\)[/tex] and [tex]\((0, 60)\)[/tex].
Therefore, the correct statement about the graph of the relationship is:
The graph is a line that goes through the points [tex]\((80, 0)\)[/tex] and [tex]\((0, 60)\)[/tex].
