First, plot the points given in the table of values. Then, try to determine what type of function the table represents.
y = 6x-2
Practice makes perfect
We are given a table of values and we need to write the equation it represents. To do so, we will start by plotting points from the table of values on the coordinate plane.
Plotting the Points
The first row from our table represents the inputs — that is, the x-values — whereas the second one represents the outputs, the y-values. Therefore, each column gives us one point (x, y) from the graph of the equation. Let's plot them all on the same coordinate plane.
As we can see, the function represented by the table is most likely linear. Let's try to find the equation of the line represented by these points.
Finding the Equation
We will write a linear equation in slope-intercept form that matches our data. This type of equation follows a specific format.
y= mx+ b
For an equation in this form, m is the slope and b is the y-intercept. Let's use two of the given points to calculate m. We will start by substituting the points into the Slope Formula. We can use any two points from the table, but this solution will use (0,- 2) and (1,4).
A slope of 6 means that for every 1 horizontal step in the positive direction we take along the graph, we move 6 vertical steps in the positive direction. Now that we know the slope, we can write a partial version of our equation.
y= 6x+ b
To complete the equation, we also need to find the y-intercept, b. Looking at the graph we made, we can see that one of our given points, (0, -2), lies on the y-axis. Since the line crosses the y-axis at this point, this point is the y-intercept. Now that we have gathered all of our missing pieces, let's write the equation that matches our table.
y= 6x+( -2)
⇔
y = 6x-2
Checking Our Answer
To check whether our function actually matches the given data, let's make a table of the given values along with the values based on our equation.
IN (x)
OUT (y)
6x -2
y
Match?
-4
-26
6( -4)-2
-26
yes
-3
-20
6( -3)-2
-20
yes
-2
-14
6( -2)-2
-14
yes
-1
-8
6( -1)-2
-8
yes
0
-2
6( 0)-2
-2
yes
1
4
6( 1)-2
4
yes
2
10
6( 2)-2
10
yes
3
16
6( 3)-2
16
yes
4
22
6( 4)-2
2
yes
As we can see, for every x-value, the y-value returned by our equation matches the output value given in the table. Therefore, we can say that our equation represents the table.
y = 6x-2
