Final answer:
The equation in slope-intercept form for the line perpendicular to y=2x-4 and passing through (0,-7) is y = (-1/2)x - 7.
Step-by-step explanation:
The student is asking to write an equation in slope-intercept form for a line that is perpendicular to the given line y=2x-4 and passes through the point (0,-7). The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
First, determine the slope of the line that is perpendicular to the given line. The slope of the original line is 2, so the slope of the perpendicular line is the negative reciprocal of 2, which is -1/2. Now, using the point (0,-7) which is the y-intercept of our new line, we can write the equation of the line as:
y = (-1/2)x - 7