Answer:
y + 2 = 4(x + 1)
8x - 2y = -4
Explanation:
When two lines coincides, their slope (m) and y-intercept (b) are of the same value, or multiples of each other.
The line, y = 4x + 2 is given in slope-intercept form, y = mx + b. Where,
slope (m) = 4
y-intercept (b) = 2.
To select which line coincides with y = 4x + 2, rewrite each given line equation in the slope-intercept form and compare teach slope and y-intercept.
Option 1: y + 2 = 4(x + 1)
y + 2 = 4x + 4
y = 4x + 4 - 2
y = 4x + 2
The slope is 4, and the y-intercept is 2, therefore it coincides with the line, y = 4x + 2.
Option 2: 4y = x + 8
4y/4 = x/4 + 8/4
y = ¼x + 2
The slope is ¼, y-intercept is 2. This line does not coincides with the line, y = 4x + 2.
Option 3: y = -4x + 2
Slope = -4 and y-intercept = 2, therefore this line doesn't coincides with the line, y = 4x + 2.
Option 4: 8x - 2y = -4
-2y = -8x - 4
-2y/-2 = -8x/-2 - 4/-2
y = 4x - (-2)
y = 4x + 2
The slope = 4, and the y-intercept = 2, therefore, it coincides with the line, y = 4x + 2.