The equation for line j can be written as 9x − y = 10. Line k is perpendicular to line j and passes through (-8, 1). What is the equation of line k in slope-intercept form?

Question

The equation for line j can be written as 9x − y = 10. Line k is perpendicular to line j and passes through (-8, 1). What is the equation of line k in slope-intercept form?

Answer 1

The first step is to find the slope of line J. The easiest way to do this is to manipulate the equation so that it is y=mx+b format, m will be the slope.

9x-y=10

Subtract 9x from both sides

9x-y-9x=10-9x

Simpllify

-y=-9x+10

Divide both sides by -1

-y/-1=(-9x+10)-1

Simplify

y=9x-10

The slope of Line J is 9, the slope of a perpendicular line is the negative reciprocal, which is m=-1/9

Next we use the point slope equation using the point given (-8,1) as (x₁,y₁)

y-y₁=m(x-x₁)

y-1=-1/9(x- -8) which simplifies to y-1=-1/9(x+8)

Now we will just need to simplify this equation to the point slope form. First, use the distributive property to clear the parenthesis.

y-1=-1/9x-8/9

Then add 1 to both sides.

y-1+1=-1/9x-8/9+9/9 (It is better to use 9/9 as 1 so that you can simplify the fractions using the common denominator)

Simplify as the last step

y=-1/9x+1/9