Question

The graph of a proportional linear equation has a slope of −35 . Which of the following points is contained on its graph?(1 point) Responses (−9,15) left parenthesis negative 9 comma 15 right parenthesis (10,6) left parenthesis 10 comma 6 right parenthesis (−10,−6) left parenthesis negative 10 comma negative 6 right parenthesis (15,−9)

Answer 1

To determine which point lies on the graph of a proportional linear equation with a slope of \(-35\), we can use the point-slope form of a linear equation, which can be expressed as:

\[ y = mx \]

where \(m\) is the slope. For this equation, we have \(m = -35\), so the equation becomes:

\[ y = -35x \]

Now, we can check each given point to see if it satisfies this equation.

1. For the point \((-9, 15)\):
\[ y = -35(-9) = 315 \]
\[ 15 \neq 315 \] (this point does not satisfy the equation)

2. For the point \((10, 6)\):
\[ y = -35(10) = -350 \]
\[ 6 \neq -350 \] (this point does not satisfy the equation)

3. For the point \((-10, -6)\):
\[ y = -35(-10) = 350 \]
\[ -6 \neq 350 \] (this point does not satisfy the equation)

4. For the point \((15, -9)\):
\[ y = -35(15) = -525 \]
\[ -9 \neq -525 \] (this point does not satisfy the equation)

None of the points provided satisfies the equation \(y = -35x\). Therefore, none of the options listed is contained on the graph of the linear equation with a slope of \(-35\).