What is an equation for the line
that passes through the point \((2,3)\)
and is parallel to the line
given by the equation \(y = -\frac{1}{2}x+7?\)
Protip: it might help the sketch
the initial line, the point,
then the new line.
What is an equation for the line
that passes through the point \((-3,5)\)
and is perpendicular to the line
given by the equation \(y = -\frac{1}{2}x+7?\)
Protip: it might help the sketch
the initial line, the point,
then the new line.
Without appealing to technology,
explain, as if convincing a skeptical peer in the class,
how you can tell that the three points
\((-1,3)\) and \((1,-1)\) and \((5,-9)\)
all lie on the same line.
Suppose a line intersects the \(x\)-axis at the number \(12,\)
and the area of the triangle formed by this line
and the positive \(x\)- and \(y\)-axis is \(30\)
What must the slope of this line be?
The price of Johnson & Johnson
(NYSE:JNJ) stock
closed at $158.48 per share on 14 August 2024,
but closed at $137.49 per share on 29 Nov 2019.
What was the average monthly change in share price
between these two dates?
What was the average annual change in share price
between these two dates?
What was the average monthly change
in gas price between these two dates?
Assuming the price of gas changed
at about this same average rate prior to January 2021,
approximately what was the price of gas for April 2000?
Using these two figures, write down an equation \(p(t)\)
of a linear function \(p\) that models the price of gas
as a function of \(t\) months since January 2021.
According to this model \(p\) what was the price of gas
at the beginning of July 2023?
We built this model using only two data points,
so maybe its not a very accurate model.
Plot the graph \(y = p(t)\) over a scatterplot
of the following data from EIA.
2021
Month
Price
January
$2.59
April
$3.25
July
$3.80
October
$3.88
2022
Month
Price
January
$3.60
April
$4.24
July
$5.10
October
$3.90
2023
Month
Price
January
$3.71
April
$3.80
July
$4.21
October
$4.00
2024
Month
Price
January
$3.01
April
$3.39
July
$3.65
October
Visually, does \(p\) appears to be an accurate model?
If not, try to adjust the parameters of the model slightly,
to make it better fit the data.
Do you think it’s a reasonable idea to use \(p\)
as a model for gas prices in the future?
I.e. do you think \(p\) can accurately predict
gas prices in the year 2025? or 2030?