Which equation fits a line that is parallel to the line y=2x+4 ?(1 point)

Question

Responses

y=2x−7
y equals 2 x minus 7

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

y=−12x+4
y equals negative Start Fraction 1 over 2 End Fraction x plus 4

y=−2x+2

Answer 1

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

Therefore, we are looking for an equation of the form \( y = 2x + b \), where \( b \) can be any number.

Now let's analyze the options provided:

1. \( y = 2x - 7 \): This has the same slope (2) and is therefore parallel.
2. \( y = \frac{1}{2}x - 3 \): This has a slope of \( \frac{1}{2} \), which is not parallel.
3. \( y = -\frac{1}{2}x + 4 \): This has a slope of \( -\frac{1}{2} \), which is not parallel.
4. \( y = -2x + 2 \): This has a slope of \( -2 \), which is also not parallel.

The only equation that fits the criteria of being parallel to \( y = 2x + 4 \) is:

\( y = 2x - 7 \).