Answer: a) y - 4 = 2/3(x) - 2
b) y - 4 = -3/2(x) -2
Explanation:
equation of original line: y = 2/3x -5
point on a line parallel to original line: (3,4)
The slope of a line parallel to a given line has the same slope, so the equation of the parallel line (in point-slope form) is:
(y - y1) = 2/3(x - x1)
point (x1, y1) is (3, 4)
plug (3,4) into the equation:
y - 4 = 2/3(x - 3)
y - 4 = 2/3(x) - 2
rewrite in slope-intercept form: y = 2/3(x) + 2
The slope of a line perpendicular to another line is the negative reciprocal of the slope of the first line: - 1/m
Therefore, the slope of the perpendicular line = -3/2
Equation for the perpendicular line is:
y - 4 = -3/2(x) -2