Which equation fits a line that is parallel to the line y=2x+4

Question

?(1 point)
Responses

y=12x−3
y equals Start Fraction 1 over 2 End Fraction x minus 3

y=−2x+2
y equals negative 2 x plus 2

y=2x−7
y equals 2 x minus 7

y=−12x+4

Answer 1

To find an equation of a line that is parallel to the line \( y = 2x + 4 \), we need to identify that parallel lines have the same slope.

The slope of the given line \( y = 2x + 4 \) is \( 2 \). Therefore, any line that is parallel to this line must also have a slope of \( 2 \).

Now, let's evaluate the given options:

1. \( y = 12x - 3 \): The slope is \( 12 \) (not parallel).
2. \( y = \frac{1}{2}x - 3 \): The slope is \( \frac{1}{2} \) (not parallel).
3. \( y = -2x + 2 \): The slope is \( -2 \) (not parallel).
4. \( y = 2x - 7 \): The slope is \( 2 \) (this is parallel).
5. \( y = -12x + 4 \): The slope is \( -12 \) (not parallel).

The only equation that has a slope of \( 2 \) and is parallel to the original line is:

\( y = 2x - 7 \).