The Graph of a Linear Equation in Two Variables

This lesson explains how to graph a linear equation in two variables, using the example x + y = 8. It covers finding solutions, plotting them on a coordinate plane, and verifying that they form a straight line. The lesson concludes by emphasizing that any point on the line is a solution, and the line represents infinite solutions.

What is the graph of a linear equation in two variables?

• A circle

• A straight line

• A set of random points

• A parabola

Which of the following is a solution to the equation x + y = 8?

• (5, 5)

• (2, 6)

• (4, 3)

• (3, 5)

What do the points plotted from the solutions of x + y = 8 form on a graph?

• A triangle

• A curve

• A straight line

• A rectangle

If a point lies on the line formed by the equation x + y = 8, what can we conclude?

• It is not a solution to the equation

• It is a solution to the equation

• It is a solution to a different equation

• It is an error in plotting

What happens to the line representing the solutions of x + y = 8?

• It curves upwards

• It stops at a certain point

• It forms a closed loop

• It extends indefinitely in both directions

How many solutions does the equation x + y = 8 have?

• One

• Two

• Five

• Infinite

What is the significance of the arrows on the line representing x + y = 8?

• They signify the line extends indefinitely

• They show the line is a ray

• They indicate the line is a segment

• They mark the endpoints of the line