Question

Line A has a slope of 3/2 and passes through the point (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? Line Aintersects line B at the point ( , ).​

Answer 1

The lines meet at (-1, -3)

Explanation:

Line A :

`(x_1, y_1) = (3, 3) \ ; \ slope, \ m_A = (3)/(2)\\\\Equation \ of \ line \ A : (y - 3) = (3)/(2)(x - 3)`

`2(y - 3) = 3(x-3)\\2y - 6 = 3x - 9\\2y = 3x - 9 + 6\\2y = 3x -3`

Line B :

`(x_2,y_2) = (-4, -2) \ ; \ slope , m_B = -(1)/(3)\\\\Equation \ of\ line \ B: (y -(-2)) = -(1)/(3)(x -(-4))`

`3(y + 2) = -1(x+4)\\3y + 6 = -x -4\\3y = -x - 4 - 6 \\3y = -x - 10`

Solve for x and y from the linear equation to find where line A and line B meets :

2y = 3x - 3 => 3x - 2y = 3 ------- (1)

3y = -x - 10 => -x = 3y + 10

=> x = - 3y - 10 --------(2)

Substitute (2) in (1) : => 3(- 3y - 10) - 2y = 3

-9y - 30 -2y = 3

-11y = 3 + 30

-11y = 33

y = -3

Substitute y in (2) : => x = -3 (-3) - 10 = 9 - 10 = -1