Have you ever studied banana plants? Take a look at this dilemma.
Mr. Thomas' class is having a discussion on the rainforest. The students have been doing some research, and now they are ready to talk about their findings.
“The vegetation of the rainforest was very interesting,” Carmen commented in Mr. Thomas’ class.
“There were so many different things growing,” Mark agreed.
The students began having a discussion about the things that had intrigued them about the plant life of the rainforest. One of the points that was brought up is that there are plants in the rainforest that can’t be found anywhere else in the world. Mr. Thomas spotted the opportunity and wrote the following problem.
You buy a banana tree that is 8 inches tall. It grows 4 inches per day. Its height (in inches)
You can express this function as an equation. This Concept will show you how to write linear equations.
Guidance
The
Take a look at this situation.
We know that we are going to use the form of the equation
This is the answer. The key is to always watch for negative signs and be sure to include them when you write your equation.
Sometimes, we can also be given the slope and a point that the line crosses through. We can also use this information to write an equation of a line.
With this example, we know the slope, so that can be easily substituted into the slopeintercept form. The point has a 0 for the
This is the answer.
What if you only know two points and you don’t know the slope? It’s a similar operation that we can use in order to write the equation.
Do you recall that the slope formula is
We will use the notion below.
if
Write the equation of the line that passes through the points
Now plug in our known values of
Do you see that we have a proportion? This can be solved by cross multiplying.
This is the answer.
What about when you have been given a table of values? Well, there is a way to figure out the equation quite simply when you have a table of values. Take a look.



0  5 
1  7 
2  9 
3  11 
4  13 
First, notice that the
Now we need to figure out the slope. Look at the y values in the table. Can you see a pattern? If you look carefully, you will see that the values jump by +2 each time. This is the slope. Think about how the line would move when graphed. The pattern of the
This is the answer.
What about function notation? Well first, think about independent and dependent variables.
In science, an independent variable is a parameter that is manipulated or chosen by a scientist while the dependent variable is a parameter that is measured. Scientists oftentimes look for a correlation between an independent variable and a dependent variable—they want to know if the dependent variable depends on the independent variable. For example, a scientist might measure the speed at which a car is moving and the force upon impact when the car hits a wall. The scientist can manipulate the speed of the car—she can make the car move slower or faster. She would then measure the force of impact related to the given speed. Then, a conclusion can be drawn about their relatedness and cars, in this case, might be designed based on that relation. The independent variable will be shown in the left column of a ttable and on the
Here we know that the function of
Write a linear equation by using the given information.
Example A
Solution:
Example B
\begin{align*}m = 4, yintercept = 6\end{align*}
Solution: \begin{align*}y=4x+6\end{align*}
Example C
\begin{align*}m = 8, yintercept = 2\end{align*}
Solution: \begin{align*}y=8x2\end{align*}
Now let's go back to the dilemma from the beginning of the Concept.
First, we need to write an equation. We can use the \begin{align*}h\end{align*} to represent the height of the banana tree. We can use the \begin{align*}d\end{align*} to represent the number of days. The 8 is the height that the tree started with. Here is our equation.
\begin{align*}h=4d+8\end{align*}
This is our answer.
Vocabulary
 Independent Variable
 a value that is not dependent on another value. It is the \begin{align*}x\end{align*} value in a table.
 Dependent Variable
 a value that is dependent on the equation. It is the \begin{align*}y\end{align*} value in a table.
 Function Notation
 an equation where the value of \begin{align*}x\end{align*} is dependent on the equation involving \begin{align*}x\end{align*}.
Guided Practice
Here is one for you to try on your own.
Write an equation in slopeintercept form with a slope of 4 and a yintercept of 13.
Solution
To do this, we can take slopeintercept form and substitute in the given values.
\begin{align*}y=mx+b\end{align*}
The \begin{align*}m\end{align*} represents the slope.
The \begin{align*}b\end{align*} represents the yintercept.
\begin{align*}y=4x+13\end{align*}
This is our answer.
Video Review
Practice
Directions: Write the equation of a line with the following slopes and \begin{align*}y\end{align*} – intercepts.
 \begin{align*}\text{slope} = 2, \ y \ \text{int} = 4\end{align*}
 \begin{align*}\text{slope} = 3, \ y \ \text{int} = 2\end{align*}
 \begin{align*}\text{slope} = 4, \ y \ \text{int} = 4\end{align*}
 \begin{align*}\text{slope} = 3, \ y \ \text{int} = 5\end{align*}
 \begin{align*}\text{slope} = \frac{1}{2}, \ y \ \text{int} = 2\end{align*}
 \begin{align*}\text{slope} = \frac{1}{3}, \ y \ \text{int} = 2\end{align*}
 \begin{align*}\text{slope} = 1, \ y \ \text{int} = 8\end{align*}
 \begin{align*}\text{slope} = 2, \ y \ \text{int} = 4\end{align*}
 \begin{align*}\text{slope} = 1, \ y \ \text{int} = 1\end{align*}
 \begin{align*}\text{slope} = 5, \ y \ \text{int} = 2\end{align*}
Directions: Write the following horizontal or vertical line equations.
 A horizontal line with a \begin{align*}b\end{align*} value of 7.
 A horizontal line with a \begin{align*}b\end{align*} value of 4.
 A vertical line with an \begin{align*}x\end{align*} value of 2
 A vertical line with an \begin{align*}x\end{align*} value of 5
Directions: Write the equation of a line that passes through the following points.
 (3, 3) and (3, 1)
 (2, 3) and (0, 3)