Question

Which statement best explains whether the following graph represents a linear or nonlinear function?

O The graph represents a nonlinear function because there is a constant rate of change.
The graph represents a nonlinear function because the rate of change is not constant.
O The graph represents a linear function because there is a constant rate of change.
O The graph represents a linear function because the rate of change is not constant.

Answer 1

The graph represents a linear function because there is a constant rate of change.

Explanation:

Linear functions have constant rate of change,

For any two points (x1, y1) and (x1, y2), rate of change remains constant, it also represents a straight line.

We know this constant as the slope of line passing through these points

`(y_2 - y_1)/(x_2 - x_1) = m`

Therefore, we can say that The graph represents a linear function because there is a constant rate of change.

Hopefully this answer helped you!!

Answer 2

(c) The graph represents a linear function because there is a constant rate of change.

Explanation:

You want to know whether the given graph represents a linear or nonlinear function, and why.

Graph

The graph shows a straight line with negative slope. We know immediately that this represents a linear function, because the graph of a linear function is a straight line. The line is straight because it has a constant rate of change.

The graph represents a linear function because there is a constant rate of change, choice C.

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Additional comment

The rate of change (slope) of the graphed curve tells the direction of the next point on the curve from the last point. When all the points have the same direction from previous points, the rate of change is constant, and the graph is a straight line.

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