Step-by-step explanation:
y = (-4/9)x + 3
-4/9 is the slope of the line. the factor is x is the slope in every line equation. the slope is always the ratio y/x.
the parallel line must have the same slope, of course.
but the y-intercept will be different.
so, its line equation looks like
y = (-4/9)x + c
we use the provided point coordinates to calculate this c.
4 = (-4/9)×9 + c
4 = -4 + c
c = 8
therefore, the parallel line equation is
y = (-4/9) + 8
a perpendicular line is a line that intercepts the original line by an angle of 90 degrees.
that means that its slope switches the original x and y, and also flips the sign.
the perpendicular slope is therefore : 9/4
so, the line equation looks like
y = (9/4)x + c
again, we use the provided point coordinates to calculate c :
4 = (9/4)×9 + c
4 = 81/4 + c
16/4 = 81/4 + c
-65/4 = c
the perpendicular line equation is
y = (9/4)x - 65/4
