Question

Which point lies on the graph of \(2 x+5 y=6 ?\) A. (-2,2) B. (3,0) C. (0,3) D. both A and B

Short answer

Based on the steps and solution, both Point A (-2,2) and Point B (3,0) lie on the graph of the equation \(2 x+5 y=6\), so the correct answer is D. Both A and B.

Step-by-step solution

Check Point A (-2,2)

Substitute the value of the point A into the equation \(2 x+5 y=6\). Therefore, if \(x=-2\) and \(y=2\), the equation becomes \(2*(-2) + 5*2\). Calculating the result we get \(6 = 6 \). Hence Point A lies on the graph.

Check Point B (3,0)

Substitute the value of the point B into the equation \(2 x+5 y=6\). Therefore, if \(x=3\) and \(y=0\), the equation add up to \(2*3 + 5*0\). Calculating, we get \(6 = 6\). Hence Point B lies on the graph.

Check Point C (0,3)

Substitute the value of the point C into the equation \(2 x+5 y=6\). Therefore, if \(x=0\) and \(y=3\), the equation becomes \(2*0 + 5*3\). After calculation, the result is \(15 ≠ 6\). Hence, Point C does not lie on the graph.