Question

Line m passes through the points (6,1) and (2,-3). Line n passes through the points (2,3) and (5,-6). Find the point intersection of these lines.

Answer 1

Since we know that m and n are lines, we can put these points into equations (slope-intercept form would be easiest), and then set the equations equal to each other to see what their x coordinate is when they intersect. 

For (6,1) and (2,-3):
slope = (y2 - y1) / (x2 - x1) = (-3 - 1) / (2 - 6) = -4 / -4 = 1

plugging this into slope-intercept form:
y = mx + b
1 = 1 x 6 + b
1 = 6 + b
b = -5
So our equation in slope intercept form is:
y = x -5

Taking the same steps for line n, we find that it's slope-intercept form is:
y = -3x + 9

If we set these two equations equal to each other, we can find the x-coordinate of the point of intersection:
-3x + 9 = x - 5
14 = 4x
x = 3.5

Plugging 3.5 back into to one of our original equations will give us the y coordinate of intersection:
y = x - 5
y = 3.5 - 5 = -1.5

Therefore, the point of intersection is (3.5, -1.5)