Linear Functions
Instructions
- First, you should watch the concept videos below explaining the topics in the section.
- Next, you should attempt to solve the exercises. You can check your answers and watch videos explaining the exercises.
- When you have finished the material below, you can start on the next section or return to the main workshop page.
Concepts
- Linear functions
- Different forms for the equation of a line
- Graphs and properties of lines
- Slope of lines
- Solving linear equations
- Solving systems of two linear equations
Linear Functions and Equations
Exercises
Directions: You should attempt to solve the problems first and then watch the video to see the solution.
- Write the equation of the line through the points \((2,4)\) and \((6,1).\)
- Kaden owns and operates a lemonade stand and is trying to find a model to predict their profits. Kaden knows that the weekly profit of the lemonade stand can be modeled by a linear function. Based on previous weeks, Kaden knows that selling 350 lemonades earns a profit of $375 for the week while selling 550 lemonades earns a profit of $875 for the week. Determine the linear profit function for Kaden's lemonade stand.
- Solve the equation \(2x+4=6.\)
- Solve the equation \(\dfrac{1}{2}x-\dfrac{3}{5}=1.\)
- Solve the equation \(3x-1=2x+5.\)
Systems of Two Linear Equations in One Variable
Exercises
Directions: You should attempt to solve the problems first and then watch the video to see the solution.
- Solve the following system of linear equations: \begin{align*} x+y&=2\\
-2x+y&=-1\end{align*}
- Solve the following system of linear equations: \begin{align*}y&=-x+2\\ y&=2x-1\end{align*}
For more examples with lines, you can see the following pages:
Section 2.1 – Review of Lines
Section 1.3 – Linear Equations in Two Variables
Section 2.1 – Review of Lines
Section 1.3 – Linear Equations in Two Variables