Final answer:
The equation of the line that passes through (6, -8) and is perpendicular to 2x - y = 7 is y = -1/2x - 4.5.
Step-by-step explanation:
To find the equation of a line that is perpendicular to another line, we need to determine the slope of the given line and then find the negative reciprocal of that slope. The given line is 2x - y = 7. We can rewrite this equation in slope-intercept form, y = mx + b, by isolating y, which gives us y = 2x - 7. Therefore, the slope of the given line is 2.
The negative reciprocal of 2 is -1/2, since the negative sign indicates the opposite direction and the reciprocal flips the fraction. So, the slope of the perpendicular line is -1/2.
Let's use the point-slope form of a linear equation, y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Plugging in the values from the given point (6, -8) and the perpendicular slope (-1/2), we get the equation of the line as y - (-8) = -1/2(x - 6). Simplifying further, we have y + 8 = -1/2x + 3.5. Rearranging the terms, the equation of the line that passes through (6, -8) and is perpendicular to 2x - y = 7 is y = -1/2x - 4.5.