Question

4. Line J has a y-intercept of 15 and passes through the ordered pair(6, -8). Line K is perpendicular to line J and passes through the orderedpair (-7,-). Which equation represents line K?AC.-y=Zx15-16fxx +B.y||||D.y563

Answer 1

B. -6/7 x - 16/3

Explanation:

The equation of a line in slope-intercept form is given by

`y=mx+b`

where m = slope and b = y-intercept.

First, let us find the equation for line J.

We are told that the y-intercept of line J is -15, meaning J passes through (0, -15). Furthermore, we are told that J also passes through (6, -8). Therefore, the slope of the line is given by

`m=(-8-(-15))/(6-0)=(7)/(6)`

Therefore, the equation for J is

`y=(7)/(6)x+b`

Now we know that the y-intercept for J is -15. Therefore, b = -15 and so the above equation gives

`y=(7)/(6)x-15`

Now, what is a line K that is perpendicular to the above line?

Here we remind ourselves that if we have an equation of the form y = mx + b, then the equation for a perpendicular line is given by

`y=-(1)/(m)x+c`

where c is a y-intercept that can be different from b.

Now in our case m = 7/6; therefore, the equation for the perpendicular line

`y=-(1)/(7/6)x+c`
`y=-(6)/(7)x+c`

Now, what is the value of c, the y-intercept?

We are told that the line K passes through the point (-7, 2/3); therefore, putting x = -7 and y = 2/3 into the above equation gives

`(2)/(3)=-(6)/(7)(-7)+c`

which simplifies to give

`(2)/(3)=6+c`

subtracting 6 from both sides gives

`(2)/(3)-6=c`
`c=-(16)/(3)`

with the value of c in hand, we can now write the equation for the line K.

`\boxed{y=-(6)/(7)x-(16)/(3).}`

which is our answer!

Looking at the answer choices we see that choice D gives the equation we found above.

Therefore, choice D is the correct answer.