Question

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



(1 point)
Responses

y=2x−1
y is equal to 2 x minus 1

y=−12x+7
y=−12x+7

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

y=−2x+3

Answer 1

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

1. If the slope of the original line is \( m \), a line perpendicular to it would have a slope of \( -\frac{1}{m} \).

Assuming that the function graph provided has a slope of \( m = 2 \) (inferred from the first option, \( y = 2x - 1 \)), the slope of the perpendicular line would be:

\[
-\frac{1}{2}
\]

Now we can examine the options to find which one has a slope of \( -\frac{1}{2} \):

1. \( y = 2x - 1 \) → slope = \( 2 \) (not perpendicular)
2. \( y = -12x + 7 \) → slope = \( -12 \) (not perpendicular)
3. \( y + 2 = 2(x - 4) \) → slope = \( 2 \) (not perpendicular)
4. \( y = -2x + 3 \) → slope = \( -2 \) (not perpendicular)

None of the provided options yield a slope of \( -\frac{1}{2} \).

However, if the slope of the line in the graph was not provided, we cannot definitively identify a perpendicular line from just the options. To answer the question accurately, it would depend on which of the previous options is present in the actual graphing function presented to you.

If the slope it referred to was 1 ( \(y = x\) ), then the perpendicular line will have a slope of -1.

If you can ascertain the slope of the original graphed line, please recheck the options to identify a slope of \( -1 \) which corresponds to it.