Lesson 4.2 Graph Linear Equations Essential Question: How do you graph linear equations?

Before we start… Community service has become a significant part of high school education. Activities can include tutoring, service projects, and partnerships with community-based organizations. Let x + y = 50 be an algebraic model for the number of hours worked, with each variable representing a different job. Write the equation in function form.

What is… a function? function form? Remember a function means that each x has only one y. Function form means that the equation is solved for y, so y will be set equal to something.

Two Variable Equations Two variable equations mean that you have both x and y in them.

What does a graph of a function tell me? A graph of an equation in two variables is the set of ALL points in a coordinate plane that represent all solutions of the equation. When you graph a line you are graphing all of the answers to it.

What is a solution of an equation? A solution of an equation with two variables is an ordered pair, (x, y) that produces a true statement when substituted in. You’ll get the same number on both sides of the equation.

Is −2,4 a solution for 𝑦=3𝑥+10?

Is 1,−3 a solution for 𝑦=−2𝑥−3?

Is 4,6 a solution for 𝑦=− 1 4 𝑥+2?

Francisco purchased x hot dogs and y hamburgers at a baseball game Francisco purchased x hot dogs and y hamburgers at a baseball game. He spent a total of $10. The equation below describes the relationship between the number of hot dogs and the number of hamburgers purchased. 3𝑥+4𝑦=10 The ordered pair 2,1 is a solution of the equation. What does the solution 2,1 represent?

Christian received a few iTunes gift cards for his birthday Christian received a few iTunes gift cards for his birthday. He went on iTunes and purchased x songs and y albums. He spent a total of $23.72. The equation bellows shows the relationship between the number of songs and the number of albums purchased. 1.29𝑥+7.99𝑦=23.72 The ordered pair 6,2 is a solution of the equation. What does the solution 6,2 represent?

Admission to the zoo is $2 each for x children and $5 Admission to the zoo is $2 each for x children and $5.50 each for y adults. The equation below describes the relationship between the number of children and the number of adults who went to the zoo. 2𝑥+5.50𝑦=17 The ordered pair 3,2 is a solution of the equation. What does the solution 3,2 represent?

How do you write an equation in function form? You will need to solve the equation for y using inverse operations. It is helpful to write an equation in function form before graphing it.

Work with your partner. Solve the following equation for y.

How can I graph a linear function? Write the equation in function form. Pick positive and negative values for x. -2 through 2 are easiest Make an x/y table. Plot the points. Connect the dots.

What is a linear equation? A linear equation is an equation whose graph is a line. Linear equations’ x variable has an exponent of 1.

Standard Form Standard form is a way to write linear equations. There are no fractions in an equation written in standard form.

Horizontal and Vertical Lines Horizontal Lines y = b These lines occur when y is equal to a constant. Parallel to the x-axis. Vertical Lines x = a These lines occur when x is equal to a constant. Parallel to the y-axis.

What makes a linear equation a function? Each x can have only one y. This means that a vertical line cannot be a function.

Running The distance d (in miles) that a runner travels is given by the function d = 6t where t is the time (in hours) spent running. The runner plans to go for a 1.5 hour run. Graph the function and identify its domain and range.

Gas Costs For gas that costs $2 per gallon, the equation C = 2g gives the cost C (in dollars) of pumping g gallons of gas. You plan to pump $10 worth of gas. Graph the function and identify its domain and range.

How do you graph linear equations?

Ticket Out the Door Solve the equation for y.