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1.2 Finding Linear Equations
Just about any real world application that has some geometric shape will have an
equation that matches. In this section, we’re interested in those shapes that are
linear.
Let’s start by looking at a linear equation (this happen to be the same one as one
of the examples in your text).
y
2
x4
3
This is a linear equation in two variables (x and y). I know it’s linear because the
exponents on the two variables are both one. I also know that “x” is the
independent variable and “y” is the dependent. (This is normally the case,
although I could solve for “x” and end up with a different equation where “y” is
independent and “x” is dependent. Let’s not go there for now.)
Cartesian coordinate system
Ordered pairs
x – coordinate y – coordinate
(2, 3)
Math96 Section 1.2 Finding Linear Equations
Find six ordered pairs. Choose values for “x” and solve for “y”.
Graph each pair.
x
y
2
x4
3
y
How many ordered pairs exist?
Compare the line with equation.
What do you notice?
What is the slope (rate of change)?
What is the y-intercept?
What is the x-intercept?
The linear equation with which we are working is in a VERY special format called
the slope-intercept form. This is because both the slope and the y-intercept are
easily found. This means we can graph this equation without calculating a single
ordered pair. “m” represents the slope, “b” represents the y-intercept
2
x4
3


slope
y-intercept
y


y  mx  b
Graph the equation again without
ordered pairs.
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Math96 Section 1.2 Finding Linear Equations
Finding the Equation from a Graph
Based on the previous discussion, for each of the following graphs, what is the
linear equation (in slope intercept form)? This only works well when the line
crosses the y-axis in a
“sweet spot”, and the
rate of change is easy to
read.
Finding the Equation from an Ordered Pair
Here is a chart that compares the cost of a rental
car with respect to the number of miles driven.
If the relationship is “perfectly linear”, the slope
between any two points (ordered pairs) will yield
the same value.
What is the slope? _________
If we are going to give the equation in “slope
intercept form” we will need the y-intercept.
The graph of the data looks like this
Although it does form a straight line, finding
the y-intercept isn’t obvious. We can guess it
to be about $40, but we can do better using
data from the table, the slope intercept form,
and the slope we just calculated. Fill in what you know and solve for “b”.
y  mx  b
When giving the final answer, consider using different
letters that match the subject of the data.
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Math96 Section 1.2 Finding Linear Equations
Example from your text:
2. Tree diameter and volume are related and of interest to foresters.
Round slopes and y-intercepts to 2 decimal places
a) Find the equation of the line passing through diameters 7.2 cm and 8.0 cm.
b) Find the equation of the line passing through diameters 8.2 cm and 9.8 cm.
c) Find the equation of the line through two representative points from the trend
line.
d) Comment on the similarities and differences in the equations you found in a – c.
Homework: Follow the directions in the text closely. Use a ruler where applicable. Try to minimize your
errors by storing values in your calculator that you will be using for subsequent parts in the problem.
Although you will be using a calculator, show your work as demonstrated/discussed in class. I f you give
me answers without work you will not receive credit. Use complete sentences, tables, lists, etc. where
applicable.
Problems: 1, 3, 5, 11
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