line a passes through the points (3,4) and (-1,2). line b passes through the points (-12,0) and (-6,-4). at what point do the lines intersect

The point of intersection of the two lines is;

(-9,-2)

Step-by-step explanation:

What we have to here is to get the equation of both lines, solve simultaneously and get the intersection points

For the first line;

The general form is

y = mx + b

formula for the slope is;

m = (y2-y1)/(x2-x1)

The points (3,4) and (-1,2)

m = (2-4)/(-1-3) = -2/-4 = 1/2

So the equation is;

y = 1/2x + b

To get b, let us substitute coordinates of the first point;

4 = 1/2 * 3 + b

4 = 3/2 + b

b = 4 - 3/2

b = (8-3)/2 = 5/2

So the equation is;

y = 1/2x + 5/2

For the second line;

Slope;

m = (-4-0)/(-6+12) = -4/6 = -2/3

The equation is;

y = -2x/3 + b

Let us substitute the first

0 = -2/3(-12) + b

0 = 8 + b

b = -8

The equation is;

y = -2x/3 - 8

Now , we want to get the intersection point

To do this, we have to solve both equations simultaneously;

Since we have an expression for y in both cases, let us equate both y

-2x/3-8 = 1/2x + 5/2

Multiply through by 6

-4x - 48 = 3x + 15

-4x-3x = 15 + 48

-7x = 63

x = 63/-7

x = -9

To get x;

Recall;

y = -2x/3 - 8

y = -2/3(-9) - 8

y = 6 - 8

y = -2