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

Answer:

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

Step-by-step 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

$m=\frac{3}{2}\\point\ (3,3)$

substitute

$y-3=\frac{3}{2}(x-3)$

Convert to slope intercept form

isolate the variable y

$y-3=\frac{3}{2}x-\frac{9}{2}$

$y=\frac{3}{2}x-\frac{9}{2}+3$

$y=\frac{3}{2}x-\frac{3}{2}$ ----> 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

$m=-\frac{1}{3}\\point\ (-4,-2)$

substitute

$y+2=-\frac{1}{3}(x+4)$

Convert to slope intercept form

isolate the variable y

$y+2=-\frac{1}{3}x-\frac{4}{3}$

$y=-\frac{1}{3}x-\frac{4}{3}-2$

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