Which line coincides with y= 4x + 2?

D. 8x - 2y = -4

Step-by-step explanation:

The line that coincides with the line represented by the equation, y = 4x + 2, is the line that has an equation that is equivalent to y = 4x + 2, or the line whose equation has the same slope (m) and y-intercept (b) as the line represented by the equation, y = 4x + 2.

A line equation is in the form of slope-intercept, is given as y = mx + b.

Thus,

The slope (m) of the line equation, y = 4x + 2, is 4, while it's y-intercept (b) is 2.

Compare each given option of line equation in their slope-intercept form, and check out which one has the same slope and y-intercept as y = 4x + 2, or has an equation equivalent to it.

Option 1: y = -4x + 2

Here, the slope (b) is -4, and y-intercept (b) is 2. This line doesn't coincide with y = 4x + 2.

Option 2: y = 4x - 2.

The slope (m) is 4, and the y-intercept (b) is -2. This line doesn't coincide with y = 4x + 2.

Option 3: 4y = x + 8

Convert to slope-intercept form

4y/4= (x + 8)/4

y = x/4 + 8/4

y = ¼x + 2

The slope is ¼. The y-intercept is 2.

This line doesn't coincide with y = 4x + 2.

Option 4: 8x - 2y = -4

Convert to slope-intercept form.

8x - 2y - 8x = -4 - 8x

-2y = - 4 - 8x

-2y/-2 = (-4 - 8x)/-2

y = -4/-2 - 8x/-2

y = 2 + 4x

y = 4x + 2

The slope is 4 and the y-intercept is 2. Therefore, 8x - 2y = -4 coincides with y = 4x + 2.