Question

I NEED HELPPP and explanation! (25 points)
The equation of line q is y=3x–2. Line r is perpendicular to line q and passes through (1,3). What is the equation of line r?

Answer 1

Answer:y=-1/3x+10/3

Step-by-step explanation:

If the line is perpendicular it means the slope is the negative reciprocal of the line. The slope of line r should be -1/3. Now the equation for line r is: y=-1/3x+b. We then can plug in values: 3=-1/3(1)+b=3=-1/3+b, b=10/3. The equation is: y=-1/3x+10/3.

Answer 2

Answer:

Step-by-step explanation:

y = 3x - 2

slope m1 = 3

Slope of line r = -1/m1 = -1/3

Equation of line in slope intercept form:  y= mx +b

$y=\dfrac{-1}{3}x+b$

Plugin x = 1 and y= 3 in the above equation.

$3=\dfrac{-1}{3}*1+b\\\\3= \dfrac{1}{3}+b\\\\\\3+\dfrac{1}{3}=b\\\\\dfrac{9}{3}+\dfrac{1}{3}=b\\\\\\b =\dfrac{10}{3}$

Equation of line r :

$y = \dfrac{-1}{3}x + \dfrac{10}{3}$