Like an equation, a graph can give us information about the relationship between quantities and the constraints on them. 

Suppose we are buying beans and rice to feed a large gathering of people, and we plan to spend $120 on the two ingredients. Beans cost $2 a pound and rice costs $0.50 a pound. If $x$ represents pounds of beans and $y$ pounds of rice, the equation $2x + 0.50y = 120$ can represent the constraints in this situation. 

The graph of $2x + 0.50y = 120$ shows a straight line. 

Graph of a line, origin O. Horizontal axis, pounds of beans, scale is 0 to 100, by 20’s. Vertical axis, pounds of rice, scale is 0 to 280, by 40’s. Line starts at 0 comma 240, passes through 10 comma 200, 30 comma 120 and 60 comma 0. Points 20 comma 80 and 70 comma 180 are shown but not on the line.

Each point on the line is a pair of $x$- and $y$-values that makes the equation true and is, thus, a solution. It is also a pair of values that satisfy the constraints in the situation.

• The point $(10,200)$ is on the line. If we buy 10 pounds of beans and 200 pounds of rice, the cost will be $2(10) + 0.50(200)$, which equals 120. 
• The points $(60,0)$ and $(45,60)$ are also on the line. If we buy only beans—60 pounds of them—and no rice, we will spend $120. If we buy 45 pounds of beans and 60 pounds of rice, we will also spend $120. 

What about points that are not on the line? They are not solutions because they don't satisfy the constraints, but they still have meaning in the situation.

• The point $(20, 80)$ is not on the line. Buying 20 pounds of beans and 80 pounds of rice costs $2(20) + 0.50(80)$, or 80, which does not equal 120. This combination costs less than what we intend to spend.
• The point $(70,180)$ means that we buy 70 pounds of beans and 180 pounds of rice. It will cost $2(70)+0.50(180)$, or 230, which is over our budget of 120.