Question

Which of the following equations represents a linear function? Question 8 options: y =6x x3 – y = –2 y =4x−−√ 2x – 4y = 6

Answer 1

Answer:

Following equations represents a linear function:

• y = 6x

• y = 4x - √2

• x – 4y = 6

Step-by-step explanation:

We know that a linear function is of the form

$y = mx+b$

where m is the rate of change or slope and b is the y-intercept.

Please note that y = mx+b represents a straight line because the degree of a linear function is always 1.

Now, let us check whether the given functions represent the linear functions or not.

Checking y = 6x

y = 6x

comparing with the equation y = mx+b

slope = 6, and y-intercept b = 0

y = 6x is a straight line because the degree of the linear equation is always 1.

Checking x³- y = -2

x³- y = -2

As the power of x variable 3. So, its graph will no longer be a straight line,

Thus, it is not a linear function as a linear function can not have any exponent.

Hence, x³- y = -2 is not a linear function.

Checking y = 4x - √2

y = 4x - √2

comparing with the equation y = mx+b

slope = 4, and y-intercept b = -√2

Thus, y = 4x - √2 is a straight line because the degree of the linear equation is always 1. Thus, the graph of y = 4x - √2 is a straight line.

Checking x – 4y = 6

x – 4y = 6

writing the in the form y = mx+b

4y = x - 6

divide both sides by 4

4y/4 = x/4 - 6/4

y = x/4 - 3/2

comparing with the equation y = mx+b

slope = x/4, and y-intercept b = -3/2

Thus, x – 4y = 6 is a straight line because the degree of the linear equation is 1. Thus, the graph of x – 4y = 6 is a straight line.

SUMMARY:

Following equations represents a linear function:

• y = 6x

• y = 4x - √2

• x – 4y = 6