Question

Find the line that is perpendicular to y=x+2
and passes through the point (3,0)
.(1 point)
Responses

y=−2x+6
y is equal to negative 2 x plus 6

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

y=12x−32
y is equal to 1 half x minus 3 halves

y=x−3

Answer 1

To find the equation of the line that is perpendicular to \( y = x + 2 \) and passes through the point \( (3, 0) \), follow these steps:

1. **Determine the slope of the given line.**
The given line \( y = x + 2 \) has a slope of \( 1 \) (the coefficient of \( x \)).

2. **Find the slope of the perpendicular line.**
The slope of a line that is perpendicular to another line is the negative reciprocal of the original slope. Since the slope of the original line is \( 1 \), the slope of the perpendicular line will be:
\[
m = -\frac{1}{1} = -1
\]

3. **Use the point-slope form of the line.**
We can use the point-slope form \( y - y_1 = m(x - x_1) \):
- Slope \( m = -1 \)
- Point \( (x_1, y_1) = (3, 0) \)
Plugging in the values:
\[
y - 0 = -1(x - 3)
\]
Simplifying this:
\[
y = -x + 3
\]

So, the equation of the line that is perpendicular to \( y = x + 2 \) and passes through the point \( (3, 0) \) is:
\[
y = -x + 3
\]

This corresponds to the second response:
- **y = −x + 3**