Question

Which of the following lines is not parallel to the graph of y = 2x + 1?6x - 3y = 22x - y = 2b. -2x = 3d. 2y- x= 2a.C.

Answer 1

The slope-intercept form of a line is given by:

$y=mx+b$

Where:

m = Slope = x-coefficient

b = y-intercept = Constant term

2 lines are parallel if:

$m1=m2$

From the line:

$y=2x+1$

The slope is 2.

Let's express every option in the slope-intercept form and let's check if they are equal to 2. If they are equal to 2, they are parallel, if not, they are not parallel.

For 6x - 3y =2:

$\begin{gathered} 6x-3y=2 \\ 3y=6x-2 \\ y=2x-\frac{2}{3} \\ so\colon \\ m1=m2 \\ 2=2 \\ _{\text{ }}true \end{gathered}$

This line is parallel to y = 2x + 1

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For 2x - y = 2:

$\begin{gathered} y=2x-2 \\ so\colon \\ m1=m2 \\ 2=2 \\ _{\text{ }}true \end{gathered}$

This line is parallel to y = 2x +1

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For y = 2x -3

$\begin{gathered} y=2x-3 \\ so\colon \\ m1=m2 \\ 2=2 \\ _{\text{ }}true \end{gathered}$

This line is parallel to y = 2x + 1

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For 2y - x = 2

$\begin{gathered} y=\frac{x}{2}+1 \\ m1=m2 \\ 2=\frac{1}{2} \\ _{\text{ }}false \end{gathered}$

This line is not parallel to y = 2x +1

Answer:

D.