Example: Write Equation of Line Given the X and Y Intercepts Write the equation of the line described below: x-intercept of 4 and y-intercept of -3.

Example: Writing an Equation from a Table Does the table below exhibit linear behavior? What is characteristic of linear behavior? Write the equation of the line that describes the above data. x y -3 8 5 3 2

Your Turn! Is the data linear? Justify. If so, then write the equation of the line describing the data. x y 1 -1 2 5 3 11

Key Concept: Direct Variation – a relationship between two variables in which one is a constant multiple of the other One variable changes in proportion to the first Constant of variation

Example: Direct Variation The variables x and y vary directly, and y = 12 when x = 4. Write and graph the equation relating x and y. Find y when x = 5.

Your Turn! The variables x and y vary directly, and y = 3 when x = 6. Write and graph the equation relating the two variables. Find x when y = -5.

Example: Writing a Linear Function from a Graph The graph shows the increase in pressure (measured in pounds per square inch) as a scuba diver descends from a depth of 10 feet to a depth of 30 feet. Pressure is the result of the weight of the column of water above the diver as well as the weight of the column of Earth's atmosphere above the water. Pressure is a linear function of depth. What is the pressure on the diver at the water's surface? Interpret the value of m in the context of the problem. Write the equation describing this linear relationship. Use the equation to determine the pressure on a diver at 20 ft.

Your Turn! The graph shows the amount of gas remaining in the gas tank of Mrs. Liu's car as she drives at a steady speed for 2 hours. How long can she drive before her car runs out of gas? Interpret the question by describing what aspect of the graph would answer the question.  Write a linear function whose graph includes the segment shown. Describe how to use the function to answer the question, and then answer the question.

Example: Writing a Linear Equation from Words For Meg’s calling plan, she pays a flat fee of $40 per month. She must pay $.05 for each text she sends. Write an equation for c, the cost of her phone each month, in terms of t, the number of texts she sends. If she sends 125 texts, how much will her phone bill be? If she has $70 per month to spend on her phone, how many texts can she send?

Your Turn! A baby weighed 8 pounds at birth and gained 1 pound each month. Write an equation for w, weight of the baby, in terms of m, months. After 7 months, how much did the baby weigh? c. When will the baby weigh 25 pounds?

Example: Write equation in Standard Form A store sells bread and milk. The price of bread is x. The price of milk is y. On Tuesday, 8 loaves of bread and 5 gallons of milk were sold for $21.40. Write an equation representing the sales for Tuesday. b. If bread costs $1.25 per loaf, how much was a gallon of milk?

Your Turn! At Jumbo’s Burger Bar, Jumbo burgers cost J each and regular cokes cost C each. Two Jumbo burgers and three regular cokes cost $5.95. Write an equation representing this. b. If one Jumbo burger costs $2.15, what is the cost of one regular coke?