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

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

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

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

(15,−9)

Answer 1

To determine which point is contained on the graph of a proportional linear equation with a slope of \(-\frac{3}{5}\), we can use the formula for a line in slope-intercept form, which is \(y = mx\) where \(m\) is the slope.

Given that the slope is \(-\frac{3}{5}\), the equation of the line is:

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

We can check each point by substituting the \(x\) value into the equation and seeing if it produces the corresponding \(y\) value.

1. **Check point \((-10, -6)\)**:
\[
y = -\frac{3}{5}(-10) = \frac{30}{5} = 6 \quad \text{(not } -6\text{, so this point is not on the line)}
\]

2. **Check point \((10, 6)\)**:
\[
y = -\frac{3}{5}(10) = -\frac{30}{5} = -6 \quad \text{(not } 6\text{, so this point is not on the line)}
\]

3. **Check point \((-9, 15)\)**:
\[
y = -\frac{3}{5}(-9) = \frac{27}{5} = 5.4 \quad \text{(not } 15\text{, so this point is not on the line)}
\]

4. **Check point \((15, -9)\)**:
\[
y = -\frac{3}{5}(15) = -\frac{45}{5} = -9 \quad \text{(this point matches)}
\]

Thus, the point that is contained on the graph of the proportional linear equation with a slope of \(-\frac{3}{5}\) is:

\((15, -9)\)