The equation of the line ef is y=2x+1. write an equation of a line parallel to line ef in slope intercept form that contains point 0,2

First, know that - 
· slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept
· parallel lines have the same slope

Given the above, the slope of line EF is 2. This means the equation of the line parallel to line EF will also have a slope of 2 (parallel lines share a slope). If we plug in our slope, the slope-intercept equation becomes y = 2x + b.

Now, we have to find b, the y-intercept. Since the line must pass through the point (0, 2), we can plug it in for the (x, y) values in our equation and solve algebraically for b.

    y = 2x + b
    2 = 2(0) + b
    2 = 0 + b
    2 = b

The y-intercept is 2. We now have the complete equation in slope-intercept form parallel to y = 2x + 1 which passes through the point (0, 2)

y = 2x + 2