Question

The graph of a proportional linear equation has a slope of − 3/5
. Which of the following points is contained on its graph?(1 point)
Responses

(15,−9)
left parenthesis 15 comma negative 9 right parenthesis

(−10,−6)
left parenthesis negative 10 comma negative 6 right parenthesis

(−9,15)
left parenthesis negative 9 comma 15 right parenthesis

(10,6)

Answer 1

A proportional linear equation can be expressed in the form \( y = mx \), where \( m \) is the slope. Since the slope is given as \( -\frac{3}{5} \), the equation can be written as:

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

We can check which of the provided points satisfies this equation.

1. For the point \( (15, -9) \):
\[
y = -\frac{3}{5}(15) = -9
\]
This point satisfies the equation.

2. For the point \( (-10, -6) \):
\[
y = -\frac{3}{5}(-10) = 6
\]
This does not satisfy the equation.

3. For the point \( (-9, 15) \):
\[
y = -\frac{3}{5}(-9) = \frac{27}{5} = 5.4
\]
This does not satisfy the equation.

4. For the point \( (10, 6) \):
\[
y = -\frac{3}{5}(10) = -6
\]
This does not satisfy the equation.

The only point that satisfies the proportional linear equation \( y = -\frac{3}{5}x \) is \( (15, -9) \).

Therefore, the correct response is:

**(15, -9)**