Creating Linear Equations from Word Problems

Creating Linear Equations from Word Problems

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Linear Equations

• y = mx + b

• y = output

• x = input

• m = slope

• b = y-intercept 

Slope

Y-Intercept

• The starting value

• The value at x=0

Writing Linear Equations

• Mr. Gill joined a gym to work off his Thanksgiving calories. The starting cost for joining the gym was $100. It costs $20 per month to stay in the gym. Write an equation to model the total cost per month.

• y = mx + b

• Total Cost = ($20)(# of months) + $100

• C = 20m + 100

Multiple Choice

Eddie joined a candle subscription cause he just couldn't get enough of that sweet cinnamon spice scent. It cost $10 to join initially. It cost $5 per month after that. Write an equation to model Eddie's total cost over time.

• C = 5m + 10

• C = 10m + 5

• C = 100 + 5

• C = 5m/10

Open Ended

Our equation was C = 5m + 10. What does the c and the m stand for here?

Multiple Choice

Xavier is addicted to riding the rails #RollingTheCoasters. He purchases a ticket to an amusement park for $10. Xavier is then charged $2 per ride (r) after that. Write an expression to model Xavier's total cost (C) after so many rides (r).

• C = 2r10

• 2 = Cr10

• C = 2r + 10

• 10 + 2 + r = 10

Open Ended

What did our C and r stand for in our last equation?

Multiple Choice

Khyla decided she was going to purchase an apple iTunes subscription. She started with $100. The subscription costed $4 each month (m). Model the total money left (T) over time.

• T = -4m100

• T = -4m + 100

• -4 = Tm + 100

• T = 100 + 4 + m

Open Ended

Why was our slope negative in the last question?

Day 2

• Equations Show Us Solutions

• Graphs show us all possible solutions

Eddies Candles

• Eddie joined a candle subscription cause he just couldn't get enough of that sweet cinnamon spice scent. It cost $10 to join initially. It cost $5 per month (m) after that. Write an equation to model Eddie's total cost over time (C).

• C = 5m + 10

• Use the equation to find the cost after any amount of months.

Eddies Candles

• C = 5m + 10

• How much money would Eddie have spend after 10 months = m?

Eddies Candles

• C = 5m + 10

• How many months (m) would it take Eddie to spend C = $35?

Multiple Choice

Sharissa goes to an arcade to get her gaming on. It costs $10 initially to get into the arcade. It costs $1 per game (g) she plays.

What equation models her total costs (C)?

• C = 2g + 10

• C = 5g + 1

• C = 1g + 10

• g = 10C

Multiple Choice

C = 1g + 10

How much will Sharissa have spend after playing 5 games (g)?

• $10

• $15

• $20

• $22

Multiple Choice

C = 1g + 10

How many games (g) will Sharissa need to play to spend $20 (C)?

• 10

• 15

• 20

• 22

Graphs Show All Solutions

Mr. Gill will show you the way

Open Ended

Jayden initially has $100. He spends $5 each day (d).

Write an equation showing how much money Jayden will have left (M) over time (days).

Money left = ?

Open Ended

Jayden's equation is:

M = -5d + 100

How much money will he have left after 14 days?

Open Ended

Jayden's equation is:

M = -5d + 100

After how many days (d) will he have $80 left?

Graphs Show All Solutions

Think about it