Answer:
D. 8x - 2y = -4
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.