Linear Functions
Instructions
- The first videos below explain the concepts in this section.
- This page includes exercises that you should attempt to solve yourself. You can check your answers and watch the videos explaining how to solve the exercises.
Concepts
- The three forms of the equation for a line: slope-intercept form, point-slope form, and standard form
- The basic properties of \(y=x\), the parent linear function, including the graph, domain, range, end behavior, slope, and \(y\)-intercept.
- The four types of linear graphs (a positive slope, a negative slope, a horizontal line, and a vertical line) and the properties of their graphs including the domain, range, and end behavior and whether the graph is increasing or decreasing.
- Writing the equation of a line through two given points
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.