Draw graphs of the equations x–y+1 = 0 and 3x+2y–12 = 0. Determine coordinates of the vertices of the triangle formed by these lines and x-axis

Question

Draw the graphs of the equations x – y + 1 = 0 and 3x + 2y – 12 = 0. Determine the coordinates of the vertices of the triangle formed by these lines and the x-axis, and shade the triangular region.

Answer 1

First equation is  x – y + 1 = 0

Add y and subtract 1 both side we get

x = y -1

Plug  y = 0 ,1 and 2 we get

x   = 0 -1   = - 1

x   = 1 -1   = 0

x    = 2 -1   =  1

X	-1	0	1
Y	0	1	2

3x + 2y – 12   = 0

Subtract 3x and add 12 both side we get

2y = 12 – 3x

Divide by 2 we get

y = 6- 1.5 x

Plug  x = 0 ,2, and 4 we get

y = 6- 1.5 *0  = 6

y = 6- 1.5 *2  = 3

y = 6- 1.5 *4  = 0

X	0	2	4
Y	6	3	0

We can see from the graphs that points of intersection of the lines with the x–axis are (–1, 0), (2, 3) and (4, 0).