Using tabular form to write an equation for a linear function
[link] relates the number of rats in a population to time, in weeks. Use the table to write a linear equation.
w , number of weeks
0
2
4
6
P(w) , number of rats
1000
1080
1160
1240
We can see from the table that the initial value for the number of rats is 1000, so
Rather than solving for
we can tell from looking at the table that the population increases by 80 for every 2 weeks that pass. This means that the rate of change is 80 rats per 2 weeks, which can be simplified to 40 rats per week.
If we did not notice the rate of change from the table we could still solve for the slope using any two points from the table. For example, using
and
Is the initial value always provided in a table of values like
[link] ?
No. Sometimes the initial value is provided in a table of values, but sometimes it is not. If you see an input of 0, then the initial value would be the corresponding output. If the initial value is not provided because there is no value of input on the table equal to 0, find the slope, substitute one coordinate pair and the slope into
and solve for
A new plant food was introduced to a young tree to test its effect on the height of the tree.
[link] shows the height of the tree, in feet,
months since the measurements began. Write a linear function,
where
is the number of months since the start of the experiment.
The ordered pairs given by a linear function represent points on a line.
Linear functions can be represented in words, function notation, tabular form, and graphical form. See
[link] .
The rate of change of a linear function is also known as the slope.
An equation in the slope-intercept form of a line includes the slope and the initial value of the function.
The initial value, or
y -intercept, is the output value when the input of a linear function is zero. It is the
y -value of the point at which the line crosses the
y -axis.
An increasing linear function results in a graph that slants upward from left to right and has a positive slope.
A decreasing linear function results in a graph that slants downward from left to right and has a negative slope.
A constant linear function results in a graph that is a horizontal line.
Analyzing the slope within the context of a problem indicates whether a linear function is increasing, decreasing, or constant. See
[link] .
The slope of a linear function can be calculated by dividing the difference between
y -values by the difference in corresponding
x -values of any two points on the line. See
[link] and
[link] .
The slope and initial value can be determined given a graph or any two points on the line.
One type of function notation is the slope-intercept form of an equation.
The point-slope form is useful for finding a linear equation when given the slope of a line and one point. See
[link] .
The point-slope form is also convenient for finding a linear equation when given two points through which a line passes. See
[link] .
The equation for a linear function can be written if the slope
and initial value
are known. See
[link] ,
[link] , and
[link] .
A linear function can be used to solve real-world problems. See
[link] and
[link] .
A linear function can be written from tabular form. See
[link] .
is it possible to leave every good at the same level
Joseph
I don't think so. because check it, if the demand for chicken increases, people will no longer consume fish like they used to causing a fall in the demand for fish
Anuolu
is not really possible to let the value of a goods to be same at the same time.....
Salome
Suppose the inflation rate is 6%, does it mean that all the goods you purchase will cost
6% more than previous year? Provide with reasoning.
Not necessarily. To measure the inflation rate economists normally use an averaged price index of a basket of certain goods. So if you purchase goods included in the basket, you will notice that you pay 6% more, otherwise not necessarily.
Good day
How do I calculate this question: C= 100+5yd G= 2000 T= 2000 I(planned)=200.
Suppose the actual output is 3000. What is the level of planned expenditures at this level of output?
I am Camara from Guinea west Africa... happy to meet you guys here
Sekou
ma management ho
Amisha
ahile becheclor ho
Amisha
hjr ktm bta ho
ani k kaam grnu hunxa tw
Amisha
belatari
Amisha
1st year ho
Amisha
nd u
Amisha
ahh
Amisha
kaha biratnagar
Amisha
ys
Amisha
kina k vo
Amisha
money as unit of account means what?
Kalombe
A unit of account is something that can be used to value goods and services and make calculations
Jim
all of you please speak in English I can't understand you're language
Muhammad
I want to know how can we define macroeconomics in one line
Muhammad
it must be .9 or 0.9
no Mpc is greater than 1
Y=100+.9Y+50
Y-.9Y=150
0.1Y/0.1=150/0.1
Y=1500
Kalombe
Mercy is it clear?😋
Kalombe
hi can someone help me on this question
If a negative shocks shifts the IS curve to the left, what type of policy do you suggest so as to stabilize the level of output?
discuss your answer using appropriate graph.