Linear Equations and Graphs

Any algebraic equation that can be converted to the form [color=#0000ff]Ax + By = C[/color] (A and B not both equal to 0) is a [color=#0000ff]linear equation in standard form[/color].[br][br]There is a postulate in Geometry that [color=#0000ff]'two points determine a line.'[/color] So it's possible to graph a linear equation by identifying two points that lie on the line. [br][br]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.[br][br]

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.

Linear Equations and Graphs

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

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.

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.

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.

Explain what this point means in this situation.

Locate the point (20, 80). 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.

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

Information: Linear Equations and Graphs