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)
Answer:
y = 2x + 2
