Unit 1: Linear Functions and Inequalities Day 3: Writing Equations of Lines

Standard and Benchmark Recognize linear, quadratic, exponential and other common functions in real-world and mathematical situations; represent these functions with tables, verbal descriptions, symbols and graphs; solve problems involving these functions, and explain results in the original context.

Standard and Benchmark Sketch graphs of linear, quadratic and exponential functions, and translate between graphs, tables and symbolic representations. Know how to use graphing technology to graph these functions.

Learning Targets a) I can sketch the graph of a linear function b) I can write a linear function. c) I can translate between the graph, table, and equation of a linear function.

Day 3: Writing Equations of Lines We have been working with the equation of a line and connecting it to the graph of the line. What if we need the same end result – the equation to the line – but are not given the graph? Can we still do it? Remember – all we need is the slope and the y-intercept. They can be found without the graph!

Writing Equations of Lines 1) Given two points, find the equation to the line in slope- intercept form Ex. (2, 1) and (0, -5) What can we get from them? The slope!!!! Once we have the slope and we already have an x and a y, we can substitute them in the slope-intercept formula and get b !!!!!

Writing Equations of Lines Lets try again. Find the slope of the line containing (4, -2) and (10, 1)

Writing Equations of Lines Now you try by yourself (-3, -1) and (3, 3)

Writing Equations of Lines How could we make this work using real life linear data? Ex. The table shows the rents and selling prices of properties from a game. Express the rent as a function of the selling price. (check to make sure it is linear) Selling Price ($) Rent ($)

Writing Equations of Lines Express the cost as a linear function of the number of items. ItemsCost ($)

Writing Equations of Lines Now you try Express the catering cost as a function of the number of people. Find the cost of catering a meal for 24 people. Number in Group Cost ($)

Writing Equations of Lines Challenge: Do we always need a table? Consider the following: Ex. Kendall’s cell phone plan charges her $25 a month plus $.05 per minute used. Write her monthly costs as a function of the minutes used. Ex. A caterer charges a $200 fee plus $18 per person served. Write the cost as a function of the number of guests.

Writing Equations of Lines Work time: WKST: WKST: Lesson 5-6 problem solving

Writing Equations of Lines Wrap up EXIT QUIZ 1) Write the equation in slope-intercept form. Then graph the line described by the equation. 6x + 2y = 10

Exit quiz cont. 2)