Solutions to Linear Equations


Explore Linear Equations in Two Variables – Solutions on the Graph.

  • Enter values of and in the yellow boxes that satisfy the given equation.
  • Click “Check” to verify your answer.
  • Click “next equation”. You can get help by checking the “Help” box to locate a point on the line and then drag to locate other points.


Graph an Equation Relating two variables.

Graph the equation you wrote relating the number of apples and the number of oranges.

(1). What is the slope of the graph?

(2). What is the meaning of the slope in terms of the context?

(B). Suppose Noah has $20 to spend. Graph the equation describing this situation.

(1). What do you notice about the relationship between this graph and the earlier one?

Let represent the first number and let represent the second number. Write an equation showing the relationship between , , and 10.


Use Linear Equations to Solve Word Problems.

You have two numbers. If you double the first number and add it to the second number, the sum is 10.

(1). Plot at least five points on this coordinate plane that make the statement and your equation true.

(2). What do you notice about the points you have plotted?

(3). List ten points that do not make the statement true.

(4). Using a different color, plot each point in the same coordinate plane.

(5). What do you notice about these points compared to your first set of points?


Match the equation  = 1.5 with its three solutions.


Select all of the ordered pairs (, ) that are solutions to the linear equation 2 + 3= 6.