Write an equation for the line that passes through (0,7) and is perpendicular to the line whose equation is y = 1/2x-1.

my answer is y = 2x-7 is this correct?

That can't be right, because when x=0, y must be 7.

Furthermore, the slope of the line you want must be -2, to be perpendicular to
y = x/2 -1, a line with slope 1/2.

Your equation has a slope of 2, not -2.

The correct answer is
(y-7)/(x-0) = -2
y = -2x + 7

To find the correct equation for the line that passes through (0,7) and is perpendicular to the line y = 1/2x - 1, follow these steps:

1. Determine the slope of the given line. The equation y = 1/2x - 1 is in slope-intercept form (y = mx + c), where m is the slope. In this case, the slope is 1/2.

2. The slope of a line perpendicular to another line is the negative reciprocal of the original line's slope. To find the slope of the perpendicular line, take the reciprocal of 1/2 (i.e., 2/1) and then change the sign to negative. Therefore, the perpendicular line has a slope of -2.

3. Now that you have the slope of the perpendicular line (-2), use the point-slope form of a line (y - y1) = m(x - x1) to write the equation. You already have one point on the line, which is (0, 7).

Substituting x1 = 0, y1 = 7, and m = -2 into the point-slope form, we get:
(y - 7) = -2(x - 0)

Simplifying the equation further:
y - 7 = -2x

4. Finally, rearrange the equation to the slope-intercept form if needed:
y = -2x + 7

Therefore, the correct equation for the line that passes through (0,7) and is perpendicular to y = 1/2x - 1 is y = -2x + 7.