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

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

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=(-1)/(3)x+b`

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

`3=(-1)/(3)*1+b\\\\3= (1)/(3)+b\\\\\\3+(1)/(3)=b\\\\(9)/(3)+(1)/(3)=b\\\\\\b =(10)/(3)`

Equation of line r :

`y = (-1)/(3)x + (10)/(3)`