Question

4

Answer 1

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