Algebra-1

To determine if the function is linear from its graph, we need to understand the characteristics of a linear function:

1. Straight Line: A linear function will always produce a straight line when graphed on a Cartesian plane.

2. Constant Rate of Change: A linear function has a constant rate of change (slope). This means that as x increases by a certain amount, y changes by a consistent amount determined by the slope m.

Let's analyze the given options in light of these characteristics:

A: "This is a linear function because it does not have a constant rate of change" - This is incorrect. Linear functions by definition have a constant rate of change (slope).

B: "This is a linear function because it creates a curved line" - This is incorrect. Linear functions always produce straight lines, not curved lines.

C: "This is a linear function because it have a constant rate of change" - This is correct. This function has a constant rate of change (slope).

Let's calculate the rate of change in y to change in x for some data points on the graph:(-1, -5) (0, -3) (1, -1) ( 3, 3).

Calculate the corresponding differences in y:

Calculate the corresponding differences in x:

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