Lesson 4.1 Writing Equations in Slope-Intercept Form Essential Question #1 Given a y-intercept & a slope can you write the equation of the line? You have a slope of -3 and a y-intercept of 4. What is the slope-intercept equation? Slope-Intercept formula: y = m x + b Substitute “-3” for m and “4” for b y = (-3) x + (4) or in function form f(x) = -3 x + 4 You try: slope: 2 Y-intercept: 9 slope: -3 Y-intercept: 0 y = 2x + 9 y = -3 x In function form: In function form f(x) = 2x + 9 f(x) = -3 x

or in function form f(x) = 2 x - 2 Essential Question #2 Given the graph of a linear function, how can you write the equation of the line? What is the slope of the line? Y2 – Y1 2 – (-2) 4 m= = = = 2 (2,2) X2 – X1 2 – (0) 2 What is the y-intercept of the line? (0,-2) (0,-2) Can you write a function for this line in slope intercept form and if so what is the function? y = mx+b or y = 2 x - 2 or in function form f(x) = 2 x - 2

Essential Question #3 Given two points can you write the equation of the line? m= Y2 – Y1 X2 – X1 Step 1: Find the slope. Step 2: Find the y-intercept. Substitute the slope m and the coordinates of one of the points into the slope-intercept form, y = mx + b, and solve for the y-intercept b. Step 3: Write an equation of the line. Substitute the slope m and the y-intercept b into the slope-intercept form, y = mx + b.

EXAMPLE Write an equation of the line that passes through the points (1, -3) and (3, 5). (x2,y2) (x1,y1) m= 5 – (-3) 3 – 1 m= 8 2 1. Find the slope. m = 4 2. Find the y-intercept. Choose one of the ordered pairs. (Either ordered pair will result in the same y-intercept) Using (1, -3) Using (3, 5) y = mx + b y = mx + b -3 = 4(1) + b 5 = 4(3) + b -3 = 4 + b 5 = 12 + b -4 -4 -12 -12 -7 = b -7 = b

m = 4 and b = -7 y = 4x - 7 EXAMPLE (continued) Substitute the slope and the y-intercept into y = mx + b m = 4 and b = -7 y = 4x - 7 EXAMPLE You try: 1. Find the equation of a line passing through the points (1, 6) and (3, -4). Steps m= (-4) – (6) 3 – 1 1) Find slope m = -5 2) Find y-intercept b (6) = -5 (1) + b b = 11 3) Write equation Y = -5x +11 or f(x) = - 5 x + 11 (in function form)

Essential Question #4 Given real-life problem, how do you model using mathematics the equation of the line? Vocabulary Linear Model – a linear function that models a real-life situation A camp program charges a registration fee and a daily amount. If the total bill for one camper was $338 for 12 days and the total bill for another camper was $506 for 19 days, how much will the bill be for a camper who enrolls for 30 days? Identify the independent variable (x) and the dependent variable (y). Since part of the bill depends on the number of days, the independent variable is the number of days. Write the two ordered pairs. (12, 338) and (19, 506) The registration fee is the y-intercept (b). This value is not known. Steps 1) Find slope 2) Find y-intercept b 3) Write equation

Find the slope and the y-intercept. m= 506 – 338 19 – 12 m= 168 7 (12, 338) (19, 506) m = 24 y = mx + b 338 = 24(12) + b y = 24x + 50 - This means that the camper pays $24 each day and a registration fee of $50. 338 = 288 + b -288 -288 50 = b If a camper is there for 30 days, find the cost. y = 24(30) + 50 y = 720 + 50 y = $770 Write a summary of what you have learned in this lesson