Question

Select the equation of a line that is perpendicular to the function graphed below



(1 point)
Responses

y+2=2(x−4)
y plus 2 is equal to 2 times open paren x minus 4 close paren

y=2x−1
y is equal to 2 x minus 1

y=−2x+3
y is equal to negative 2 x plus 3

y=−12x+7

Answer 1

To determine which equation represents a line that is perpendicular to the function graphed, we need to know the slope of the original function. Lines that are perpendicular have slopes that are negative reciprocals of each other.

1. **Identify the slope of the original function.**
If the slope of the original line is \( m \), then the slope of a line that is perpendicular would be \( -\frac{1}{m} \).

2. **Check the slopes of the provided equations:**
- For \( y + 2 = 2(x - 4) \), rearranging gives \( y = 2x - 10 \), so the slope is \( 2 \) (perpendicular slope is \( -\frac{1}{2} \)).
- For \( y = 2x - 1 \), the slope is also \( 2 \) (perpendicular slope is \( -\frac{1}{2} \)).
- For \( y = -2x + 3 \), the slope is \( -2 \) (perpendicular slope is \( \frac{1}{2} \)).
- For \( y = -12x + 7 \), the slope is \( -12 \) (perpendicular slope is \( \frac{1}{12} \)).

3. **Select the correct equation based on the slope.**
Without the original slope, assuming it's \( 2 \), the lines \( y + 2 = 2(x−4) \) and \( y = 2x−1 \) are not perpendicular.

The line that has a slope of \( -2 \) (from \( y = -2x + 3 \)) would be perpendicular to a function with a slope of \( \frac{1}{2} \), which is not expressed in the options above.

Therefore, without seeing the actual plot, the best choice from the provided options for a potentially perpendicular slope to any positive slope seems to be \( y = -2x + 3 \) (as it has a negative slope).

The answer is: **y = −2x + 3**.