Student Page 2.7.4 Finding Equations from Representations
Directions: Tables, graphs (use grid points!), and stories are provided. For each case:
Find the slope.
Find the \(y\)-intercept.
Write an equation.
Explain how you know the slope and \(y\)-intercept are correct. Check 2 points in your equation to show it is correct.
1.
(a) Linear Function Representation.
| \(x\) | \(y\) |
|---|---|
| 0 | 4 |
| 2 | 9 |
| 4 | 14 |
| 6 | 19 |
| 8 | 24 |
(b) Slope.
Say how you know you are correct.
(c) \(y\)-intercept.
Say how you know you are correct.
(d) Equation.
Answer:
2.
(a) Linear Function Representation.
| \(x\) | \(y\) |
|---|---|
| 6 | 11 |
| 9 | 9 |
| 12 | 7 |
| 15 | 5 |
| 18 | 3 |
(b) Slope.
Say how you know you are correct.
(c) \(y\)-intercept.
Say how you know you are correct.
(d) Equation.
Answer:
3.
(a) Linear Function Representation.
(b) Slope.
Say how you know you are correct.
(c) \(y\)-intercept.
Say how you know you are correct.
(d) Equation.
Answer:
4.
(a) Linear Function Representation.
(b) Slope.
Say how you know you are correct.
(c) \(y\)-intercept.
Say how you know you are correct.
(d) Equation.
Answer:
5.
(a) Linear Function Representation.
Hannah shelters her dog at Happy Trails Kennel while she is out of town. Happy Trails requires Hannah to begin each month with $200 in her account and charges her account $15 each day her dog stays at the kennel. What amount, \(A\text{,}\) will Hannah have in her account at the end of the month if her dog stays at the kennel for \(d\) days?
(b) Slope.
Say how you know you are correct.
(c) \(y\)-intercept.
Say how you know you are correct.
(d) Equation.
Answer:
6.
(a) Linear Function Representation.
What is the total cost, \(C\text{,}\) of \(x\) months of use of the Fitness Fun health club? Fitness Fun charges a $75 initiation fee plus $20 per month.
(b) Slope.
Say how you know you are correct.
(c) \(y\)-intercept.
Say how you know you are correct.
(d) Equation.
Answer: