WRITING LINEAR EQUATIONS Lesson 8.2 Notes

You try ! On the grid provided plot the following points. K (2, 1)L (3, 3)M (0, 5)N (4, 0) K L M N

Write a linear equation to represent a given situation Caleb is x years old. His sister is 10 years older than he is. If his sister is y years old, write an equation that relates their two ages. The problem says that the sister’s age is the variable y. So we can write the equation. The equation is called a equation. y = x + 10 linear

Independent and Dependent Variables y = x + 10 x is called the variable y is called the variable because the value of y on the value of x. We are expressing y x. In terms of x tells us x is the independent variable! independent dependent depends in terms of

A rhombus has sides of length r centimeters. If the perimeter of the rhombus is P centimeters, express P in terms of r. P = 4r Expressing P in terms of r means that r is the variable and P is the variable. independent dependent

Write an equation and state the independent and dependent variables. Hannah took p minutes to jog around a park. Sofia took 12 minutes longer to job around the park. If Sofia took t minutes to jog around the park, express t in terms of p. Equation: Independent Variable: Dependent Variable: t = p + 12 t p

Write an equation and state the independent and dependent variables. A bouquet of roses costs $30. A bouquet of tulips cost m dollars less. If the cost of one bouquet of tulips is n dollars, express n in terms of m. Equation: Independent Variable: Dependent Variable: n = 30 – m n m

Write an equation and state the independent and dependent variables. Nathan has 7 boxes of marbles. Each box contains b marbles. If he has c marbles altogether, express c in terms of b. Equation: Independent Variable: Dependent Variable: c = 7b7b7b7b c b

Write an equation and state the independent and dependent variables. A motel charges Mr. Kim x dollars for his stay. Mr. Kim stayed at the motel for 12 nights. If the rate per night for a room is y dollars, express y in terms of x. Equation: Independent Variable: Dependent Variable: y = y x

Use tables and graphs to represent linear equations. The length of a rectangular picture frame is 5 inches longer than its width. Write and equation to show how its width and length are related. l = w + 5 The length is dependent on the width. The width (w) is the variable and the length (l) is the variable. Many pairs of l and w will make this equation true. independent dependent

Use tables and graphs to represent linear equations. We can use a table to show possible values of the independent and dependent variables for the equation. l = w + 5 We can graph the data using the ordered pairs,,,, and on a coordinate plane. (1, 6) (2, 7) (3, 8) (4, 9) (5, 10)

Use the horizontal axis for the independent variable and the vertical axis for the dependent variable. Horizontal Independent Vertical Dependent

All linear equations have graphs that are. The graph of an equation contains all the ordered pairs that make the equation true. The point (2.5, 7.5) is the on the graph of the equation l = w + 5. l = w = lines

Each can of paint contains 5 gallons of paint. Write an equation to show the relationship between the number of cans of paint and the volume of paint. Let v represent the volume of paint in gallons, and c represent the number of cans of paint. Equation: We can organize data in a table. The volume of paint depends on the number of cans. The volume is the dependent variable. v = 5c5c5c5c Number of Cans (c) Volume of Paint (v gallons)

Number of Cans (c) Volume of Paint (v gallons) We can write the data in the table as ordered pairs and plot them on a coordinate plane. Always use the horizontal axis for the independent variable. Number of Cans c v Volume of Paint (gal)

The graph of the equation v = 5c contains all the ordered pairs that make the equation true. Number of Cans c v Volume of Paint (gal)