Question 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

Answer: 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 Reply

Answer:

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