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1. The equations of the lines l1 with points (-2, 5), and (-1, -10) and the line l2 with points (5, 15), and (3, 8), gives the coordinate of the intersection between the lines as the point; (-45/37, -250/37)

   Which method can be used to describe the lines to find the intersection point?

   The slope, m1, of line 1 l1 is found as follows;

   • m1 = (5 – (-10))/(-2- (-1)) = -15

   The equation of line l1 in point and slope form is therefore;

   y1 – 5 = -15•(x – (-2))

   Which gives;

   y1 = -15•(x – (-2)) + 5 = -15•x – 25

   • y1 = -15•x – 25

   The slope, m2, of line 2 l2 is found as follows;

   m2 = (15 – 8)/(5 – 3) = 3.5

   Equation of line l2 is therefore;

   y2 – 15 = 3.5•(x – 5)

   Which gives;

   y2 = 3.5•(x – 5) + 15 = 3.5•x – 2.5

   • y2 = 3.5•x – 2.5

   At the intersection point, we have;

   y1 = y2

   Therefore;

   -15•x – 25 = 3.5•x – 2.5

   18.5•x = -22.5

   x = -22.5/18.5 = -45/37

   y2 = 3.5•x – 2.5

   At the intersection point, we have;

   y = y2 = 3.5×(-22.5/18.5) – 2.5 = -250/37

   y = -250/37

   The coordinates of the intersection between the lines is therefore;

   • (-45/37, -250/37)

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