Linear Equations and Graphs

Any algebraic equation that can be converted to the form Ax + By = C (A and B not both equal to 0) is a linear equation in standard form. There is a postulate in Geometry that 'two points determine a line.' So it's possible to graph a linear equation by identifying two points that lie on the line. To get these points, assign a small input value to x which yields an output value to y resulting in an ordered pair. Repeat to get another ordered pair.

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, write an equation

Draw the graph to represent the equation you wrote above.

Each point on the line is a pair of x - and y -values that make the equation true and is thus a solution. It is also a pair of values that satisfy the constraints in the situation. Write a point that is a solution to this equation.

Explain what this point means in this situation.

Locate the point (20, 80). Explain what this point means in this situation.

Is (20, 80) a solution to the equation? Explain.

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