Identify Linear Functions: Examining y = mx + b Properties

Video Solution

Solution Steps

00:00 Which representations describe a linear function?

00:03 Let's arrange it to match the pattern of a linear function

00:12 We can see that the function is linear according to the pattern

00:17 Open parentheses properly, multiply by each term

00:24 Collect terms

00:29 Compare to the pattern of a linear function

00:34 The slope of the function is 0, and the y-intercept is (-4)

00:38 Therefore, this function is linear

00:45 This function is not linear, X is squared

00:48 The same applies in this case, X is cubed

00:51 And this is the solution to the question

Step-by-Step Solution

To solve this problem, we'll examine each expression to see if it represents a linear function:

Option A: $y = 5 - 3x$ .
This expression fits the linear form $y = mx + c$ with $m = -3$ and $c = 5$ . Hence, it is a linear function.
Option B: $y = -4(x+1) + 4x$ .
First, expand the expression:
$-4(x+1) = -4x - 4$ .
Substituting, we get $y = -4x - 4 + 4x$ , which simplifies to $y = -4$ .
This is a linear function where $y = c$ (a constant term with zero slope).
Option C: $y = -3x^2 + 2$ .
The term $-3x^2$ indicates a quadratic expression, as the highest power of $x$ is 2. Therefore, it is not a linear function.
Option D: $y = 6 + x^3$ .
The term $x^3$ shows a cubic expression since the highest power of $x$ is 3, thus not a linear function.

Clearly, only options A and B describe linear functions. Therefore, the correct answer is:

Answers A and B are correct.