Question

Theequationforlineucanbewrittenasy = 6x + 6 . Line v , whichisperpendiculartoline u , includes the point (10, –5) . What is the equation of line v ? Write the equation in slope-intercept form. Write the numbers in the equation as proper fractions, improper fractions, or integers.

Answer 1

Answer:

$y=\frac{-1}{6}x-\frac{10}{3}$

Step-by-step explanation:

Slope intercept form of the equation of a line is $y=mx+b$ where m denotes the slope of line and $b$ denotes the y-intercept.

Equation of a line u is $y=6x+6$

Here, slope of line u = m = 6

As the line v is perpendicular to line u, product of slopes of both the lines is equal to $-1$.

Slope of line v  $=\frac{-1}{6}$

So, slope intercept form of the line v is $y=\frac{-1}{6}x+b$

As point $(10,-5)$ lies on the line v, put $(x,y)=(10,-5)$ in equation $y=\frac{-1}{6}x+b$

$-5=\frac{-1}{6}(10)+b\\-5=\frac{-5}{3}+b\\ -5+\frac{5}{3}=b\\\frac{-15+5}{3}=b\\\\\frac{-10}{3}=b$

Equation of line v is $y=\frac{-1}{6}x-\frac{10}{3}$