A line passes through the points 40 and 06 Another line has

A line passes through the points (-4,0) and (0,6). Another line has a gradient of value -2 and passes through the point (6,7). You are required to find the coordinates of the point of intersection of the two lines.

What is the x coordinate of the point of intersection?

What is the y coordinate of the point of intersection? Give your answer as a number only correct to AT LEAST TO THREE DECIMAL PLACES

Solution

Equation of 1st line:

Slope of line = (y-6)/(x-0) = (6-0)/(0+4) = 1.5
y-6 = 1.5x
y-1.5x = 6....1

Slope of 2nd line:

(y-7)/(x-6) = -2
y-7+2x-12 = 0
2x+y=19.......2

Solve the 1,2 to get answers for i) and ii)

y-1.5x= 6...1
2x+y = 10...2

i.

Subtracting equation 1 from 2:

3.5x =4

x= 4/3.5 = 1.143

So, y-1.5*1.143 = 6

ii.

y = 6+1.5*1.143 = 7.715
y = 7.715