Start by using the Slope Formula to find the slope of the linear relationship.
x
10
20
30
40
y
10
15
20
25
Practice makes perfect
We are given the following table with data that represents a linear relationship.
x
10
20
40
y
10
15
20
We want to find the missing data in the table. To do so we will use the Slope Formula.
Finding the Slope
Let's start by using the Slope Formula to find the slope of the linear relationship.
m = y_2- y_1/x_2- x_1In this formula, ( x_1, y_1) and ( x_2, y_2) are two points on the line and m is the slope of a line. Since the data represents the linear relationship, we can read the points from the table. We will find the slope using the points ( 10, 10) and ( 20, 15).
We obtained that the slope is equal to 5. Now we can use the Slope Formula to find the missing data. Let's consider the points (x,20) and (40,y), where x and y are the unknown values. We can use the value of the slope and, for instance, the point (10,10) to find the values of x and y one at a time.
Finding the Value of x
To find the value of x we will substitute ( 10, 10) into ( x_1, y_1) and
( x, 20) into ( x_2, y_2) in the Slope Formula. Recall that m= 12.
1/2 = 20- 10/x- 10
Now we can solve the obtained equation for x to find its value.
To find the value of y we will substitute ( 10, 10) into ( x_1, y_1) and
( 40, y) into ( x_2, y_2) in the Slope Formula. Recall that m= 12.
1/2 = y- 10/40- 10
Now we can solve the obtained equation for y to find its value.
