Question

Line l1 passes through (-2, 5), and (-1, -10)
Line l2 passes through (5,15), and (3,8).

Find the coordinates of the intersection between the lines. Show all of your work.

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)