Question

line A has A slope of 3/2 and passes through (3,3) .line b has a slope of -1/3 and passes through the point (-4,-2). at what point does line A intersect line B ?

Answer 1

The line A intersect line B at point (-1,-3)

Explanation:

step 1

Find the equation of the Line A

the equation of a line in point slope form is equal to

`y-y1=m(x-x1)`

we have

`m=(3)/(2)\\point\ (3,3)`

substitute

`y-3=(3)/(2)(x-3)`

Convert to slope intercept form

isolate the variable y

`y-3=(3)/(2)x-(9)/(2)`

`y=(3)/(2)x-(9)/(2)+3`

`y=(3)/(2)x-(3)/(2)` ----> equation A

step 2

Find the equation of the Line B

the equation of a line in point slope form is equal to

`y-y1=m(x-x1)`

we have

`m=-(1)/(3)\\point\ (-4,-2)`

substitute

`y+2=-(1)/(3)(x+4)`

Convert to slope intercept form

isolate the variable y

`y+2=-(1)/(3)x-(4)/(3)`

`y=-(1)/(3)x-(4)/(3)-2`

`y=-(1)/(3)x-(10)/(3)` ----> equation B

step 3

Solve the system of equations A and B by graphing

The intersection point both graphs is the solution of the system

using a graphing tool

The line A intersect line B at point (-1,-3)

see the attached figure