To determine which point lies on the graph of the equation [tex]\( r = \frac{3}{4}b \)[/tex], we can substitute each point into the equation and check if it satisfies the equation.
### Checking Point A: [tex]\(\left(\frac{3}{4}, 1\right)\)[/tex]
1. Substitute [tex]\( r = \frac{3}{4} \)[/tex] and [tex]\( b = 1 \)[/tex] into the equation:
[tex]\[
r = \frac{3}{4} \cdot b
\][/tex]
2. Substitute the values:
[tex]\[
\frac{3}{4} = \frac{3}{4} \cdot 1
\][/tex]
3. Simplify the right-hand side:
[tex]\[
\frac{3}{4} = \frac{3}{4}
\][/tex]
4. This is a true statement, so point A lies on the graph.
### Checking Point C: [tex]\((3, 4)\)[/tex]
1. Substitute [tex]\( r = 3 \)[/tex] and [tex]\( b = 4 \)[/tex] into the equation:
[tex]\[
r = \frac{3}{4} \cdot b
\][/tex]
2. Substitute the values:
[tex]\[
3 = \frac{3}{4} \cdot 4
\][/tex]
3. Simplify the right-hand side:
[tex]\[
3 = 3
\][/tex]
4. This is a true statement, so point C also lies on the graph.
### Checking Point D: [tex]\((0, \frac{3}{4})\)[/tex]
1. Substitute [tex]\( r = 0 \)[/tex] and [tex]\( b = \frac{3}{4} \)[/tex] into the equation:
[tex]\[
r = \frac{3}{4} \cdot b
\][/tex]
2. Substitute the values:
[tex]\[
0 = \frac{3}{4} \cdot \frac{3}{4}
\][/tex]
3. Simplify the right-hand side:
[tex]\[
0 = \frac{9}{16}
\][/tex]
4. This is a false statement, so point D does not lie on the graph.
Based on our calculations, the points that lie on the graph of the equation [tex]\( r = \frac{3}{4}b \)[/tex] are:
- Point A: [tex]\(\left(\frac{3}{4}, 1\right)\)[/tex]
- Point C: [tex]\((3, 4)\)[/tex]
Thus, the point that would be on the graph that represents this proportional relationship is A [tex]\(\left(\frac{3}{4}, 1\right)\)[/tex].
