Question

The equation of line EF is y = x + 6. Write an equation of a line parallel to line EF in slope-intercept form that contains point (0, −2).

Answer 1

To find a line parallel to y = x + 6 that passes through (0, -2), maintain the same slope of 1 and solve for the y-intercept using the given point. The resulting equation for the parallel line is y = x - 2.

Step-by-step explanation:

The given equation y = x + 6 represents a line with a slope of 1. A line parallel to it would have the same slope. To write an equation for a line parallel to y = x + 6 that goes through the point (0, −2), we use the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.

Since the slope m must be the same for parallel lines, m = 1. We then use the given point to solve for b. Therefore, we plug x = 0 and y = −2 into the equation:

y = mx + b
−2 = (1)(0) + b
b = −2

So the equation of the line parallel to y = x + 6 and passing through (0, −2) is y = x −2.

Answer 2

Y=x-2 is the answer I think