Writing Linear Equations
Write the equation for line a.
y=1/2x+2
A truck is shipping jugs of drinking water and cases of paper towels. A jug of drinking water weighs 40 pounds and a case of paper towels weighs 16 pounds. The truck can carry 2,000 pounds of cargo altogether.
a. If the truck is carrying 10 jugs of drinking water, how many cases of paper towels can they carry?
b. If the truck is carrying 50 cases of paper towels, how many jugs of drinking water can they carry?
a. 100 cases of paper towels
b. 30 jugs of drinking water
How many solutions does the following system of equations have?
y=-2x+5
y=-2x-2
No solutions
Sketch a scatter plot that has a positive association.
Scatter plot that has points that generally show that as x increases, y increases
Write the equation for b.
y=-2/3x + 5
A truck is shipping jugs of drinking water and cases of paper towels. A jug of drinking water weighs 40 pounds and a case of paper towels weighs 16 pounds. The truck can carry 2,000 pounds of cargo altogether.
Write an equation relating the number of jugs of water (w) and the number of cases of paper towels (t) the truck can carry.
40w+16t=2000
How many solutions does the following system of equations have?
x+y=11
3x+3y=33
Infinitely Many
Sketch a scatter plot that has a negative association.
Scatter plot that has points that generally show that as x increases, y decreases
When is a relationship proportional?
A relationship is proportional when the rate is constant AND it begins at (0,0).
Write the equation for line c.
y=1/4x-3
A pizza shop charges $12 per pizza and a delivery fee of $5. How much would Mrs. Johnson pay if she ordered 7 pizzas for the staff at Carmody?
$89
The solution to the system:
x = 4y
2x + 3y = 22
(8,2)
A scatter plot shows some data comparing the wingspan of a butterfly to its body length. Would you expect this scatter plot to have a positive or negative association?
Positive association
A successful music app tracked the number of song downloads each day for a month for 4 music artists, represented by lines ℓ, j, m, and d over the course of a month. Which line represents an artist whose downloads remained constant over the month?
Artist m
Write the equation for lines d and e.
d: y=7
e: x=-2.5
A pizza shop charges $12 per pizza and a delivery fee of $5. How much would x pizzas cost?
y=12x+5
The solution to the system
y = 3x - 1
7x + 2y = 37
(3,8)
A scatter plot shows some data comparing the wingspan (mm) of a butterfly to its body length (mm). A linear model of y = 0.238x + 4.642 where x is wingspan and y is body length can be fit to this data. Interpret the slope in the context of the problem.
A butterfly's body length can be expected to increase 0.238 mm for every 1 mm increase in wingspan.
Noah is growing three different types of trees. He is keeping track of the height of each tree over time.
Which tree grows the slowest?
Tree 3
What are the steps for writing an equation in slope intercept form from a line on a graph?
1. Find the y-intercept (starting point)
2. Determine the slope by creating a slope triangle and doing rise divided by run
3. Put the slope in for m and the y-intercept in for b into y=mx+b
A pizza shop charges $12 per pizza and a delivery fee of $5. Describe what a graph where the x axis is representing the number of pizzas and the y axis is representing the total cost would look like.
The y-intercept would be at 5 and the line would increase by 12 for each additional pizza.
The solution to the system
3s - 2t = 4
t = 2s - 1
(-2,-5)
A scatter plot shows some data comparing the wingspan (mm) of a butterfly to its body length (mm). A linear model of y = 0.238x + 4.642 where x is wingspan and y is body length can be fit to this data. According to this model, what body length will a butterfly be expected to have for a wingspan of 60 mm.
18.922 mm
A pool holds 19,900 gallons of water. There are two hoses that can be used to fill the pool, a large one and a small one. On an average day, it takes 5 hours to fill the pool with the large hose and 12 hours with the small hose. Which graph best represents this scenario?
A