Question

Match the equations with their correct type of functions.

• A. Slope = 4 and linear
• B. Non-linear function
• C. Slope= 16 and linear

Answer 1

All linear functions can be represented in the form of y = mx + c, where m = slope of the linear function and b = y-intercept.

In first option, y = 4x + 3

Here,
rate of change = 4 and it is constant.
power of x = 1

So, y = 4x + 3 is a linear function with slope = 4.


In second option,
$y=\frac{1}{x}\left(3\right)+2$
$\Rightarrow y=3x^{-1}+2$

As per the condition of linear function, y = mx + c, the power of 'x' should be 1.
But the above function has a power of x as -1.

$\text{So,}y=\frac{1}{x}\left(3\right)+2\text{is a non-linear function}$


In third option,
$y=5(3x+2)+x$
$\Rightarrow y=16x+10$

Rate of change = 16 and it is constant.
Power of x = 1.

So, y = 5(3x + 2) + x is a linear function with slope = 16.