Answer(s):
Perpendicular: y - 5 = [tex]\frac{-5}{3}[/tex](x + 1)
Parallel: y - 5 = [tex]\frac{3}{5}[/tex](x + 1)
I have graphed all three of the equations, see attached.
Perpendicular Explanation:
A perpendicular line will have the opposite reciprocal slope of the given line's slope. We will transform this equation into slope-intercept form (y = mx + b, where m is the slope and b is the y-intercept).
-3x + 5y = 9 ➜ [tex]\displaystyle y = \frac{3}{5} x+\frac{9}{5}[/tex]
This gives us a slope of negative five-thirds. NNext, we will take this slope and substitute the given coordinate point into it to create our final equation in point-slope form (y - y1 = m(x - x1) where (x1, y1) is a coordinate point on the graph and m is the slope).
y - 5 = [tex]\frac{-5}{3}[/tex](x + 1)
Parallel Explanation:
A parallel line will have the same slope as the given line. We will transform this equation into slope-intercept form (y = mx + b, where m is the slope and b is the y-intercept).
-3x + 5y = 9 ➜ [tex]\displaystyle y = \frac{3}{5} x+\frac{9}{5}[/tex]
This gives us a slope of three-fifths. Next, we will take this slope and substitute the given coordinate point into it to create our final equation in point-slope form (y - y1 = m(x - x1) where (x1, y1) is a coordinate point on the graph and m is the slope).
y - 5 = [tex]\frac{3}{5}[/tex](x + 1)
