Question

Select the equation of a line that is perpendicular to the function graphed below:
graph shows a line going through (0.5,0) (0.-1)


(1 point)
Responses

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

x+2y=14
x plus 2 y is equal to 14

y=2x−1
y is equal to 2 x minus 1

y=−2x+3

Answer 1

To find the equation of a line that is perpendicular to the given line, we first need to determine the slope of the line that is currently graphed using the points (0.5, 0) and (0, -1).

The slope \( m \) of a line is given by the formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using the points \((x_1, y_1) = (0.5, 0)\) and \((x_2, y_2) = (0, -1)\):

\[
m = \frac{-1 - 0}{0 - 0.5} = \frac{-1}{-0.5} = 2
\]

The slope of the line given is \( 2 \). The slope of a line that is perpendicular to it is the negative reciprocal:

\[
m_{\text{perpendicular}} = -\frac{1}{2}
\]

Now, we need to find the equation of a line with slope \( -\frac{1}{2} \). Looking at the options provided:

1. \( y + 2 = 2(x - 4) \) → slope = 2 (not perpendicular)
2. \( x + 2y = 14 \) → rearranging gives \( y = -\frac{1}{2}x + 7 \) → slope = -\frac{1}{2} (perpendicular)
3. \( y = 2x - 1 \) → slope = 2 (not perpendicular)
4. \( y = -2x + 3 \) → slope = -2 (not perpendicular)

The correct equation of the line that is perpendicular to the original line is:

**\( x + 2y = 14 \)**