This topic covers: - Intercepts of linear equations/functions - Slope of linear equations/functions - Slope-intercept, point-slope, & standard forms - Graphing linear equations/functions - Writing linear equations/functions - Interpreting linear equations/functions - Linear equations/functions word problems
When distances, prices, or any other quantity in our world changes at a constant rate, we can use linear functions to model them. Let's learn how different representations, including graphs and equations, of these useful functions reveal characteristics of the situation.
Linear equations word problems: volcano Linear equations word problems: earnings Modeling with linear equations: snow Linear function example: spending money Fitting a line to data
The standard form for linear equations in two variables is Ax+By=C. For example, 2x+3y=5 is a linear equation in standard form. When an equation is given in this form, it's pretty easy to find both intercepts (x and y). This form is also very useful when solving systems of two linear equations.
Think of linear as just a line. A linear function is one that, when graphed, forms a line. Linear functions are in the form: f(x) = ax + b, where a and b are constants.
If we want to write a linear function that represents this, the first thing to discuss is what you want x and y to be. The question tells us that y should be the account's value, and x should be the number of movies rented. From here, all we do is fill out slope-intercept form (y = mx+b).
About this unit We can write linear equations in different forms to reveal different features of the scenarios they describe. Let's get clever. Unit guides are here! Power up your classroom with engaging strategies, tools, and activities from Khan Academy’s learning experts. PDF
