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 this graph:

The graph is a straight line sloping upwards from left to right.

 

Slope:

Let's calculate the ratios of change in y to change in x for some data points on the graph:(-2, -7) (0, -4) (2, -1) ( 6, 5).

Calculate the corresponding differences in y:

 

Calculate the corresponding differences in x:

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