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Algebra 1 Name: _______________________________ Unit 3: L1 Date: _________________ Period: _______ Writing Equations of Lines in SIF and Standard Form (5.1, 5.2 , 5.6) Essential Question: What information is needed to determine the equation of a line? Goal: 1) I can use slope-intercept form to write an equation of a line. 2) I can write a linear equation in standard form. Vocabulary: Slope-Intercept Form: when equations in two variables (x, y) are solved for y, we can immediately identify the slope and the y-intercept of the graph. Formula: y mx b Slope: the _____________ of the x term (m) and should stay as a fraction (no mixed numbers) Y-Intercept: the ______________ term and where the line crosses the y-axis (b) 2) Standard Form: Formula: Ax + By = C The coefficient of x cannot be ________________ i. To undo this multiply everything on both sides by (-1) No ________________ or decimals can be present. A, B, and C all must be whole numbers. i. To clear fractions ___________________ everything on both sides by the least common denominator. 3) Parallel Lines: Two lines that never intersect NEW… Two lines are parallel if they have the ____________________ slope. Steps for Slope-Intercept Form: 1) S lope - Find m 2) I ntercept - Find b 3) F orm - Put in y=mx+b form. Steps for Standard Form: 1) Write in Slope-Intercept Form (SIF) First 2) Convert to Standard Form Section 1: GIVEN SLOPE AND Y-INTERCEPT… Write the equation of the line in SIF and Standard Form. PROBLEM 1) slope = -5 y-intercept = -2 S I F Standard PROBLEM 2) slope = S I F Standard 3 2 y-intercept = 0.25 3) m = 0 b= 4 4) m = 1 5 b=0 Section 2: GIVEN SLOPE AND A POINT… Write the equation of the line in SIF and Standard form. PROBLEM 5) slope = -2 passes through (6 , -3) S I F Standard F Standard 6) m = undefined passes through (2 , -2) 7) m = 1 2 passes through (5 , 6) 8) m = 0 passes through (-7 , 1) Section 3: PARRALEL… Write the equation of the line in SIF and Standard Form PROBLEM 9) parallel to y 2 x2 3 passes through (-2 , 1) S I // to 1 y x2 4 10) passes through (-3 , 2) 11) // to y 5 passes through (8 , 4) Section 4: Keystone Applications 12) A plumber charges $66 for the first hour of a service call and $45 for any additional hours. YT 12) A rental company charges a flat fee of $30 and an additional $0.25 per mile to rent a moving van. A. Write a linear model of this situation in slopeintercept form. A. Write an equation to model the total charge in slope-intercept form. B. Rewrite your equation from (A) into standard form. B. Rewrite your equation from (A) into standard form. C. Determine the cost of a 3-hour call. C. Determine the price of the rental if you drove 102 miles Homework: pg 276 # 3 – 8 all & pg 282 # 3-10all & pg 311 # 7-9 all Lesson summary / Ticket Out: A) Describe the procedure for writing an equation of a line in slope-intercept form. What are the 3 steps? Is there a helpful way to remember these steps? B) What are the rules for standard form? C) What is significant about the slopes of two parallel lines?