Mr. Deyo Solving Problems by Writing Equations in Point-Slope Form MS Algebra A-F-IF-7 – Ch. 6.3b Solving Real World Problems with the Point-Slope Form Mr. Deyo Solving Problems by Writing Equations in Point-Slope Form

By the end of the period, I will apply the Title: 6.3b Apply Point-Slope Form to Solve Real World Problems Date: Learning Target By the end of the period, I will apply the point-slope form to write equations and solve real world problems. I will demonstrate this by completing Four-Square Notes and by solving problems in a pair/group activity.

Home Work 1-2-3: 1) Class 4-Square Notes Put In Binder? 2) Section 6.3 Pg. 345-346 3) Section ______ TxtBk.Prob.#45-49 ALL Notes Copied on blank sheet Solved and Put in Binder? of paper in Binder? Table of Contents Date Description Date Due

Storm Check (Think, Write, Discuss, Report) Questions on which to ponder and answer: How are the two images similar? How are they different? How can these two images be related to math? IMAGE 1 IMAGE 2

Daily Warm-Up Exercises Step 1: Find the slope between 2 points Daily Warm-Up Exercises Step 2: Find the value of b using m and 1 point For use with pages xxx–xxx Step 3: Write general y = mx + b equation A golf course charges an yearly membership fee of $800 and a greens fee of $8 for each round of golf play that year. One year you spent $920. How many rounds of golf did you play that year? Rounds Costs $800 1 $808 ?? $920

Daily Warm-Up Exercises Step 1: Find the slope between 2 points Daily Warm-Up Exercises Step 2: Find the value of b using m and 1 point For use with pages xxx–xxx Step 3: Write general y = mx + b equation A golf course charges an yearly membership fee of $800 and a greens fee of $8 for each round of golf play that year. One year you spent $920. How many rounds of golf did you play that year? Step 1 808–800 8 8 m = = = Rounds Costs $800 1 $808 ?? $920 1 - 0 1 Step 2 800 = 8(0) + b 800 = 0 + b 800 = b Step 3 y = mx + b (920) = (8)x + 800 920 = 8x + 800 120 = 8x ANSWER x = 15

Vocabulary Slope y-intercept Data Pair Slope-Intercept Form Point-Slope Form

Vocabulary Acquisition Friendly Definition Sketch Wordwork Sentence DAY 2 1. Review word Friendly Definition Physical Representation 2. Draw a sketch DAY 1 Use Visuals Introduce the word Friendly Definition Physical Representation Use Cognates Write friendly definition Word List Vocabulary Acquisition DAY 3 and/or DAY 4 1. Review the word Friendly Definition Physical Representation 2. Show how the word works Synonyms/antonym Word Problems Related words/phrases Example/non-example DAY 5 1. Review the word Friendly definition Physical Representation 3. Write a sentence at least 2 rich words (1 action) correct spelling correct punctuation correct subject/predicate agreement clear and clean writing

How To Get To Point-Slope Form Notes: Given One Point & SLOPE Step 1) Plug m and one point into y – Y1 = m(x – X1) x y X1 Y1 Step 2) Solve for y (if you want slope-intercept form)

B) Find the cost of 9000 flyers. Problem A ADVERTISING Solve a multi-step problem You have color flyers printed to advertise your band, _______________. You pay $225 for the first 1000 flyers plus $80 for every 1000 extra flyers. A) Write an equation that gives the total cost (in dollars) of the flyers as a function of the number (in thousands) of flyers that you buy. B) Find the cost of 9000 flyers.

= C + 80F 145 = C1 – C F1 F m ) ( = – C 1 F 80 ) ( 225 = – C 80 F 225 Problem A SOLUTION Solve a multi-step problem STEP 1 Identify the rate of change and a data pair. Let C be the total cost (in dollars) and F be the number of flyers (in thousands). Rate of change, m: $80 per 1 thousand extra flyers Data pair ( F1, C1 ) : 1 thousand flyers, $225 STEP 2 Write an equation using point-slope form. Rewrite the equation in slope-intercept form so that the total cost is a function of the number of flyers. = C1 – C F1 F m ) ( Write point-slope form. = – C 1 F 80 ) ( Substitute 80 for m, 1 for F1, and 225 for C1. 225 = – C 80 F 225 Solve for C. = C + 80F 145 C = 80F + 145 C = 80 (9) + 145 C = 720 + 145 C = $865 STEP 3 Find the cost of 9000 stickers. ANSWER The cost of 9000 stickers is $865.

Problem B ADVERTISING WHAT IF? Solve a multi-step problem WHAT IF? Suppose a second company charges $250 for the first 1000 flyers. The cost of each additional 1000 flyers is $60. A) Write an equation that gives the total cost (in dollars) of the flyers as a function of the number (in thousands) of flyers ordered. B) Find the cost of 9000 flyers. Which company charges less for 9000 flyers?

C = 60F + 190 C = $730 C – C1 = M (F – F1) C – 250 = 60 (F – 1) Problem B ADVERTISING Solve a multi-step problem WHAT IF? Suppose a second company charges $250 for the first 1000 flyers. The cost of each additional 1000 flyers is $60. A) Write an equation that gives the total cost (in dollars) of the flyers as a function of the number (in thousands) of flyers ordered. B) Find the cost of 9000 flyers. Which company charges less for 9000 flyers? C – C1 = M (F – F1) C – 250 = 60 (F – 1) C – 250 = 60F – 60 C = 60F + 190 C = 60F + 190 C = 60(9) + 190 C = 540 + 190 C = $730 ANSWER ANSWER The 2nd company charges less.

Storm Check (Think, Write, Discuss, Report) If you are given the slope and one point, how can you create a linear equation that is in point-slope form? (2-3 sentences) When given the slope and one point, I can create a linear equation in point-slope form by _____________ _______________________________________________ ______________________________________________.

By the end of the period, I will apply the Title: 6.3b Apply Point-Slope Form to Solve Problems Date: Learning Target By the end of the period, I will apply the point-slope form to write equations and solve real world problems. I will demonstrate this by completing Four-Square Notes and by solving problems in a pair/group activity.

Home Work 1-2-3: 1) Class 4-Square Notes Put In Binder? 2) Section 6.3 Pg. 345-346 3) Section ______ TxtBk.Prob.#45-49 ALL Notes Copied on blank sheet Solved and Put in Binder? of paper in Binder? Table of Contents Date Description Date Due

m = How To Get To Point-Slope Form Y2 – Y1 X2 – X1 X1 Y1 X2 Y2 Notes: Given Two Points x y X1 Y1 X2 Y2 Step 1) Make a table Use the two points to calculate SLOPE (m) Y2 – Y1 m = X2 – X1 Step 2) Plug m and one point into y – Y1 = m(x – X1) Step 3) Solve for y (if you want slope-intercept form)

m = HORSE RANCH Problem A Write a real-world linear model from a table HORSE RANCH Problem A The table shows the cost of visiting a horse ranch for one day and night for different numbers of people. Can the situation be modeled by a linear equation? Explain. If possible, write an equation that gives the cost as a function of the number of people in the group. Number of People 4 6 8 10 12 Cost (dollars) 250 350 450 550 650 STEP 1 m = STEP 2 C – C1 = M(P – P1)

C = 50P + 50 m = 50 C – C1 = M(P – P1) C – 250 = 50(P – 4) Write a real-world linear model from a table HORSE RANCH Problem A SOLUTION The table shows the cost of visiting a horse ranch for one day and night for different numbers of people. Can the situation be modeled by a linear equation? Explain. If possible, write an equation that gives the cost as a function of the number of people in the group. Number of People 4 6 8 10 12 Cost (dollars) 250 350 450 550 650 STEP 1 Find the rate of change for consecutive data pairs in the table. STEP 2 Use point-slope form to write the equation. Let C be the cost (in dollars) and p be the number of people. Use the data pair (4, 250). 450 – 550 8 10 = 50, C – C1 = M(P – P1) C – 250 = 50(P – 4) C – 250 = 50P – 200 C = 50P + 50 650 – 550 = 50 12 – 10 m = 50 Because the cost increases at a constant rate of $50 per person, the situation can be modeled by a linear equation.

C – C1 = M(W – W1) m = Problem B MAILING COSTS The table shows the cost of sending a single piece of first class mail for different weights. Can the situation be modeled by a linear equation? Explain. If possible, write an equation that gives the cost of sending a piece of first class mail as a function of its weight. Weight (ounces) 1 Cost (dollars) 4 5 10 12 0.39 1.11 1.35 2.55 3.03 m = C – C1 = M(W – W1) Step 1) Step 2)

C = 0.24W + 0.15 m = 0.24 C – C1 = M (W – W1) C – 0.39 = 0.24(W – 1) Problem B MAILING COSTS The table shows the cost of sending a single piece of first class mail for different weights. Can the situation be modeled by a linear equation? Explain. If possible, write an equation that gives the cost of sending a piece of first class mail as a function of its weight. Weight (ounces) 1 Cost (dollars) 4 5 10 12 0.39 1.11 1.35 2.55 3.03 C – C1 = M (W – W1) C – 0.39 = 0.24(W – 1) C – 0.39 = 0.24W – 0.24 C = 0.24W + 0.15 m = 1.35 – 1.11 5 – 4 m = 0.24 / 1 m = 0.24 Step 1) Step 2) Yes, because the cost increases at a constant rate of $.24 per ounce; C = 0.24W + 0.15 ANSWER

Storm Check (Think, Write, Discuss, Report) If you are given a table of data points, how can you determine if you can use a linear equation to model the situation? (2-3 sentences) When given a table of data points, I can determine if I can use a linear equation to model the situation by _______________________________________________ ______________________________________________.

Vocabulary Slope y-intercept Data Pair Slope-Intercept Form Point-Slope Form

By the end of the period, I will apply the Title: 6.3b Apply Point-Slope Form to Solve Problems Date: Learning Target By the end of the period, I will apply the point-slope form to write equations and solve real world problems. I will demonstrate this by completing Four-Square Notes and by solving problems in a pair/group activity.

Home Work 1-2-3: 1) Class 4-Square Notes Put In Binder? 2) Section 6.3 Pg. 345-346 3) Section ______ TxtBk.Prob.#45-49 ALL Notes Copied on blank sheet Solved and Put in Binder? of paper in Binder? Table of Contents Date Description Date Due

Ticket OUT. Write an equation of the line that passes through the points (1, 5) and (4, –1). Step 1: Find the slope between 2 points x y Step 2a: Plug m and 1st point into Point-Slope Form Step 2b: Plug m and the 2nd point into the Point-Slope Form Turn to your partner and share your answer. Please use correct answer. Partner B, please share what Partner A told you.

-2 m = = = y – y1 = m(x – x1) y – 5 = -2(x – 1) y – y2 = m(x – x2) Ticket OUT. Write an equation of the line that passes through the points (1, 5) and (4, –1). Step 1: Find the slope between 2 points x y 4 -1 1 5 -1 - 5 -6 -2 m = = = 4 - 1 3 Step 2a: Plug m and 1st point into Point-Slope Form Step 2b: Plug m and the 2nd point into the Point-Slope Form Turn to your partner and share your answer. Please use correct answer. Partner B, please share what Partner A told you. y – y1 = m(x – x1) y – 5 = -2(x – 1) y – y2 = m(x – x2) y + 1 = -2(x – 4)