Objectives:
- I can write a linear equation from a given graph.
- I can write a linear equation from a given table of values.
- I can write a linear equation from two given points.
What is a linear equation?
A linear equation has two variables that when graphed it creates a straight line. Earlier you learned about
slope-intercept form. We can write linear equations in slope-intercept form so that it is easier for us to graph the equation.
Recall: We call it slope-intercept form because it is organized as that we can easily locate the slope and
y-intercept of the line. For example, the general equation for slope-intercept form is:
A linear equation has two variables that when graphed it creates a straight line. Earlier you learned about
slope-intercept form. We can write linear equations in slope-intercept form so that it is easier for us to graph the equation.
Recall: We call it slope-intercept form because it is organized as that we can easily locate the slope and
y-intercept of the line. For example, the general equation for slope-intercept form is:
In this form, we can easily spot the slope, m, and the y-intercept, b.
SLOPE: You have learned previously that the slope is the steepness of a line. You have heard the phrase "rise over run" many times now, also known as the change in y over the change in x.
Y-INTERCEPT: The y-intercept is the value of "y" when the line intercepts the y-axis.
SLOPE: You have learned previously that the slope is the steepness of a line. You have heard the phrase "rise over run" many times now, also known as the change in y over the change in x.
Y-INTERCEPT: The y-intercept is the value of "y" when the line intercepts the y-axis.
Writing Linear Equations from a Graph
In order to write the linear equation of a graph, we need to know two things: (1) Where does the line cross the
y-axis, and (2) what is the slope of the line. We will use these two pieces of information and plug them into the slope-intercept form equation. This will create a linear equation. Let's look at the steps to follow and an example:
y-axis, and (2) what is the slope of the line. We will use these two pieces of information and plug them into the slope-intercept form equation. This will create a linear equation. Let's look at the steps to follow and an example:
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Practice #1
Determine the equation of the following graph:
Click HERE to check your answer!
Writing Linear Equations from a Table
Earlier, you learned how to graph an equation given in slope-intercept form. However, what if you are given a linear equation that is not in slope-intercept form? We have already discussed earlier that slope-intercept form makes it easier to recognize the slope and y-intercept. Hence, we will need to "convert" any linear equation into slope-intercept form. In other words, "solve for y"!
Let's look at an example:
Let's look at an example:
Now we can graph the equation since it is in slope-intercept form!
Practice #4
Graph the following equation:
Click HERE to check your answer!
Quiz
You will take the quiz after you have researched and taken notes on slope-intercept form.
CLICK HERE FOR QUIZ
CLICK HERE FOR QUIZ