Mathematics
Grade-8
Easy
Question
Four (x, y) pairs of a certain function are shown in the table below. Which of the following best describes the function?
- The function increases linearly
- The function decreases linearly
- The function is constant
- The function is not linear
Hint:
Linear functions are those whose graph is a straight line.
A linear function has the following form
y = f(x) = a + bx
A linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y.
a is the constant term or the y intercept. It is the value of the dependent variable when x = 0.
b is the coefficient of the independent variable. It is also known as the slope and gives the rate of change of the dependent variable.
The correct answer is: The function increases linearly
A linear function has one independent variable and one dependent variable. Increasing function is a mathematical function whose value is increases as the independent variable. It increases over a given range. As shown in the question, For increasing value of x the value of y is also increasing.
let Function f(x) = mx+ c
Put the value of coordinates (-3,1) & (-1,4) in linear function f(x) = mx+ c that is given in question.
1 = (-3)m + c ...... eq(1)
&
4 = (-1)m + c ..... eq(2)
After solving eq(1) & eq(2) ,we get
m(slope) = 3/2 and c = 11/2
The slope is a constant 
between any two points and is positive; so, y increases as x increases.
Therefore, it is increasing linearly.
A linear function has one independent variable and one dependent variable. For example, consider the function y = 2x. By choosing a value for x we can use this to calculate a value for y. Thus x is the independent variable and y is the dependent variable.
