Final answer:
To find the equation of the line that is perpendicular to 4x – 3y = 18 and passes through (8, -8), rearrange the given equation to find its slope, compute the negative reciprocal for the perpendicular line's slope, and then use the point-slope formula with the perpendicular slope and given point.
Step-by-step explanation:
The student has asked for the equation of a line that passes through the point (8, -8) and is perpendicular to the line represented by the equation 4x – 3y = 18. To find this equation, we first need to identify the slope of the given line and then use the negative reciprocal of that slope for our perpendicular line. We start by rearranging the given equation into slope-intercept form (y = mx + b) where m is the slope and b is the y-intercept.
4x – 3y = 18 can be rearranged as y = (4/3)x – 6, so the slope (m) of the given line is 4/3.
The slope of the line perpendicular to the given line is the negative reciprocal of 4/3, which is -3/4.
Using the point-slope form (y – y1) = m(x – x1) with the point (8, -8) and the slope -3/4, we get y + 8 = -3/4(x – 8). Simplifying, we get y + 8 = -3/4x + 6, and finally, the equation of our perpendicular line is y = -3/4x – 2.