Question

Which of the following equations represents the given graph?

• A. 2x+y=6
• B. y+2x+4
• C. 2(x-1)+3y=4
• D. 2x-3y=6

Answer 1

The correct option is C 2(x-1)+3y=4

The two points obtained from the graph are: (0, 2) and (3, 0)
Let us take a linear equation in two variables as: ax + by + c = 0
The equation can be written as : $y=mx+c$
Substituting the value of abscissa and ordinate from the given two points:
0 = 3m + c
2 = 0 + c
Solving these two equations, we get: c = 2 and $m=\frac{-2}{3}$
Substituting the value of m and c in the second equation, we get,
$y=\frac{-2x}{3}+2$, which can also be written as,
$3y+2x=6$