Question

From the choices given below, choose the equation whose graphs are given in the figures:

• A. $y=x+2$
• B. $y=x-2$
• C. $y=-x+2$
• D. $x+2y=6$

Answer 1

The correct option is C

$y=-x+2$

Explanation for the correct option:

Option C: $y=-x+2$

The equation which is satisfied all the given points on the graph is the required equation.

For point $\left(0,2\right)$; $2=0+2$

For point $\left(2,0\right)$; $0=-2+2$

For point $\left(-1,3\right)$; $3=-\left(-1\right)+2$

For all the above points $\mathrm{LHS}=\mathrm{RHS}$

Hence, this equation is correct for this graph.

Explanation for the incorrect options:

Option A: $y=x+2$

For point $\left(0,2\right)$; $2=0+2$

For point $\left(2,0\right)$; $0\ne 2+2$

Option B: $y=x-2$

For point $\left(0,2\right)$; $2\ne 0-2$

Option D: $x+2y=6$

For point $\left(0,2\right)$; $0+2\left(2\right)\ne 6$

Hence, the correct option is option C.