Write the equation of a line in slope-intercept form that is perpendicular to the line y = three-fifths x minus 1 and passes through the point (-9, 4).
A. five-thirds x plus 19
B. three-fifths x plus forty-seven-fifths
C. negative five-thirds x minus 11
D. negative five-thirds x plus 19

Question

Write the equation of a line in slope-intercept form that is perpendicular to the line y = three-fifths x minus 1 and passes through the point (-9, 4).
	A.	five-thirds x plus 19
	B.	three-fifths x plus forty-seven-fifths
	C.	negative five-thirds x minus 11
	D.	negative five-thirds x plus 19

anonymous · Answer

please help this is my last one and im desperate  medal to best answer

mathstudent55 · Answer

You are given the line
$y = \dfrac{3}{5} x - 1$

This given line has slope $\dfrac{3}{5} $.

Ok so far?

mathstudent55 · Answer

What is the slope of a perpendicular line?

anonymous · Answer

y = (3/5)x - 1
Slope is 3/5
The slopes of perpendicular lines are negative reciprocals, so
(3/5) m = -1
m = -5/3

So the new slope is -5/3.
The new line passes through (-9, 4)

y-4 = -5/3(x--9)
y-4 = -5/3(x+9)
y = -5/3x + 19

anonymous · Answer

Wait a minute sorry I multiplied wrong.
It should be
y-4 = -5/3x -15
y = -5/3x - 11
So the answer is C not D. Careful with negative signs when distributing!
Also thanks for the medal mathstudent!

mathstudent55 · Answer

You can also do it this way.

Once you know the slope of the perpendicular, since you need the answer in slope-intercept form, you can use the slope-intercept equation with the slope of the perpendicular, and with the given point plugged in for x and y. Then you solve for b.

$y = mx + b$

We know that for the perpendicular, $m = - \dfrac{5}{3} $

Use the given point (-9, 4) and the slope to get:

$4 = -\dfrac{5}{3} (-9) + b$

$4 = 15 + b$

$b = -11$

Final answer is:

$y = - \dfrac{5}{3} - 11$