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.

answer 1 : option "c"

answer 2 : option "d"

answer 3 : option "b"

answer 4 : option "d"

answer 5 : option "b"

answer 6 : option "a"

answer 7 : option "c"

answer 8 : option "d"

answer 9 : option "c"

answer 10 : option "d"

answer 11 : option "c"

answer 12 option "b"

answer 13 option "c"

answer 14 option "c"

answer 15 option "d"

answer 16 option "a"

answer 17 option "b"

answer 18 option "c"

answer 19 option "a"

answer 20 option "a"

answer 21 option "c"

d