Question

Write an equation of a line parallel to line ef in slope-intercept form that contains point (0, 2).

1) y = -2x - 4
2) y = -1/2x - 4
3) y = 2x + 2
4) y = 1/2x + 2

Answer 1

To find a parallel line to ef that passes through (0, 2), we use the slope of -2 from line ef and the y-intercept from the point given, resulting in the equation y = -2x + 2.

Step-by-step explanation:

Finding a Parallel Line in Slope-Intercept Form

To write an equation of a line parallel to line ef that contains the point (0, 2), we first need to determine the slope of line ef. The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. The given line ef, option 1) y = -2x - 4, has a slope of -2. A line parallel to this will have the same slope. Now, since our line passes through the point (0, 2), this point is the y-intercept of our new line. Therefore, the equation of the line is simply
y = -2x + 2, which isn't listed among the options provided.