Final answer:
To find the equation of a line perpendicular to the given line, we first rewrite the equation in slope-intercept form. Then, we find the negative reciprocal of the given slope to get the slope of the perpendicular line. Finally, we use the point-slope formula to find the equation of the line passing through a given point and having the perpendicular slope.
Step-by-step explanation:
To find the equation of a line perpendicular to a given line, we need to determine the slope of the given line and then use that slope to find the perpendicular slope.
Given: 2x + 5y = 4y - 7
Rewriting the equation in slope-intercept form, y = mx + b, we get:
5y - 4y = -2x - 7
y = -2x - 7
Comparing this equation to y = mx + b, we see that the slope (m) is -2.
The slope of a line perpendicular to this line is the negative reciprocal of the given slope, which is 1/2.
Now, we have the slope (m = 1/2) and a point the line passes through (-8,12).
Using the point-slope formula, y - y1 = m(x - x1), we can plug in the values to find the equation of the line:
y - 12 = (1/2)(x + 8)
y - 12 = (1/2)x + 4
y = (1/2)x + 16
Therefore, the equation of the line passing through (-8,12) and perpendicular to 2x + 5y = 4y - 7 is y = (1/2)x + 16.