General
General
Easy
Question
Determine the linear function from the data in the table.
Hint:
We are given a table of values of x and f(x). Using the values, we have to write a linear function. A linear function is a function where the highest degree of variables is 1. The variables can be multiplied by constants. The operation between variables is addition or subtraction.
The correct answer is:
We will write y = f(x)
For this question, we will use the slope intercept form
The slope intercept form is y = mx + c
Here, y and x are the given values. The variable “m” represents a slope or the rate of change of the values. The variable “c” is the y-intercept.
Using the values from given table, we will find the values of m and c.
From the table we can see that y is decreasing by 6. And, x is changing by value 1.
The equation becomes y = -6x + c.
To find the value of c, we will substitute one of the ordered pair of x and y in the given equation.
Let’s substitute x = 0 and y = 180
y = -6x + c
180 = -6(0) + c
c = 180
We will substitute this value in the above equation.
y = -6x + 180
Therefore, the linear equation for the given table is f(x) = -6x + 180.
A linear equation when plotted on graph gives a line. For such questions, we should know about the slope intercept form.
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