Question

Which ordered pairs represent points on the graph of this equation? Select all that apply.

x= 3/5 y

( -5,3)
( -3,-5)
( 3,5)
( -5,-3)
( 5,-3)
( 3,-5)

Answer 1

To determine which ordered pairs represent points on the graph of the equation \( x = \frac{3}{5}y \), we can rearrange this equation to express \( y \) in terms of \( x \):

\[
y = \frac{5}{3}x
\]

Now we can check each ordered pair (x, y) to see if it satisfies the equation \( x = \frac{3}{5}y \).

1. For the point \((-5, 3)\):
\[
-5 = \frac{3}{5}(3) \Rightarrow -5 = \frac{9}{5} \quad \text{(False)}
\]

2. For the point \((-3, -5)\):
\[
-3 = \frac{3}{5}(-5) \Rightarrow -3 = -3 \quad \text{(True)}
\]

3. For the point \((3, 5)\):
\[
3 = \frac{3}{5}(5) \Rightarrow 3 = 3 \quad \text{(True)}
\]

4. For the point \((-5, -3)\):
\[
-5 = \frac{3}{5}(-3) \Rightarrow -5 = -\frac{9}{5} \quad \text{(False)}
\]

5. For the point \((5, -3)\):
\[
5 = \frac{3}{5}(-3) \Rightarrow 5 = -\frac{9}{5} \quad \text{(False)}
\]

6. For the point \((3, -5)\):
\[
3 = \frac{3}{5}(-5) \Rightarrow 3 = -3 \quad \text{(False)}
\]

The ordered pairs that satisfy the equation \( x = \frac{3}{5}y \) are:
- \((-3, -5)\)
- \((3, 5)\)

So the correct answers are:
- (-3, -5)
- (3, 5)