4.6: Intercepts and the CoverUp Method
Suppose you had a cat, and you gave him 1 treat per day. What if you wanted to graph the number of treats left in his treat jar as a function of the number of days that have passed? You could do it if you knew the intercepts, but how would you find them? One way would be to use the CoverUp Method. In this Concept, you'll learn all about the CoverUp method so that you can create graphs such as this.
Guidance
In the last Concept, you saw how to find intercepts by substituting the value of zero in for one of the variables.
To find the
To find the
This method works for any form of linear equations.
A second method of finding the intercepts is called the CoverUp Method. Using the Multiplication Property of Zero
Example A
Graph
Solution: To solve for the
To solve for the
Now graph by first plotting the intercepts and then drawing a line through these points.
Example B
Jose has $30 to spend on food for a class barbeque. Hot dogs cost $0.75 each (including the bun) and burgers cost $1.25 (including bun and salad). Plot a graph that shows all the combinations of hot dogs and burgers he could buy for the barbecue, spending exactly $30.
Solution: Begin by translating this sentence into an algebraic equation. Let
Find the intercepts of the graph. This example will use the CoverUp Method. Feel free to use substitution if you prefer.
By graphing Jose’s situation, you can determine the combinations of hot dogs and burgers he can purchase for exactly $30.00.
Understanding the CoverUp Method
The coverup method simply removes one variable at a time, in order to solve for the other variable. The solutions are then the intercepts, since removing a variable, or "covering up" a variable, is the same thing as setting it equal to zero. Try out this concept in the example below:
Example C
Graph
Solution:
First start by "covering up"
When
Now, "coverup"
When
Now graph the equation by plotting the two intercepts and connecting them with a line.
Guided Practice
Graph
Solution:
First start by "covering up"
When
Now, "coverup"
When
Now graph the equation by plotting the two intercepts and connecting them with a line.
Practice
Sample explanations for some of the practice exercises below are available by viewing the following video. Note that there is not always a match between the number of the practice exercise in the video and the number of the practice exercise listed in the following exercise set. However, the practice exercise is the same in both. CK12 Basic Algebra: Graphing Using Intercepts (12:18)
 Explain the process of the CoverUp Method.
 Do you prefer the Substitution Method or the CoverUp Method? Why?
Find the intercepts of the following equations using the CoverUp Method.

5x−6y=15 
3x−4y=−5 
2x+7y=−11 
5x+10y=25
In 7 – 18, use any method to find the intercepts and then graph the equation.

y=2x+3 
6(x−1)=2(y+3) 
x−y=5 
x+y=8  \begin{align*}4x+9y=0\end{align*}
 \begin{align*}\frac{1}{2} x+4y=12\end{align*}
 \begin{align*}x2y=4\end{align*}
 \begin{align*}7x5y=10\end{align*}
 \begin{align*}4xy=3\end{align*}
 \begin{align*}xy=0\end{align*}
 \begin{align*}5x+y=5\end{align*}
 \begin{align*}7x2y=6\end{align*}
 What needs to be done to the following equation before you can use either method to find its intercepts? \begin{align*}3(x+2)=2(y+3)\end{align*}
 At the local grocery store, strawberries cost $3.00 per pound and bananas cost $1.00 per pound. If I have $10 to spend between strawberries and bananas, draw a graph to show what combinations of each I can buy and spend exactly $10.
 A movie theater charges $7.50 for adult tickets and $4.50 for children. If the $900 theater takes in ticket sales for a particular screening, draw a graph that depicts the possibilities for the number of adult tickets and the number of child tickets sold.
 In football, touchdowns are worth 6 points, field goals are worth 3 points, and safeties are worth 2 points. Suppose there were no safeties and the team scored 36 points. Graph the situation to determine the combinations of field goals and touchdowns the team could have had.
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intercept
The point at which a graphed equation crosses an axis. The intercept is an ordered pair at which the line crosses the axis (the horizontal axis). Its ordered pair has the form . The intercept is an ordered pair at which the line crosses the axis (the vertical axis). Its ordered pair has the formImage Attributions
Here you'll learn how to use the CoverUp Method to determine the @$\begin{align*}x\end{align*}@$intercept and the @$\begin{align*}y\end{align*}@$intercept of a graph.