Answers

1. 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

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