Linear Graph Analysis: Determining Uniform vs Non-uniform Rate of Change

Video Solution

Solution Steps

00:06 First, we ask, is the rate of change uniform?

00:11 Let's pick some points on the graph and have a look.

00:18 Notice how the change between each pair of points stays the same.

00:46 That means the graph shows a uniform rate of change.

00:49 And there you go, that's the solution to our question!

Step-by-Step Solution

To solve this problem, let's analyze the graph of the line:

Step 1: Identify two points on the line. For simplicity, let's choose the intercept at $x = 1$ and $y = 3$ , and another at $x = 6$ and $y = 0$ (assuming these are easily readable points).
Step 2: Calculate the slope using the formula $\frac{y_2 - y_1}{x_2 - x_1}$ .
Step 3: Substituting in our chosen points, the slope is $\frac{0 - 3}{6 - 1} = \frac{-3}{5}$ .
Step 4: Since the graph is a straight line and the slope is constant, the rate of change is uniform.

Therefore, the graph shows a constant or uniform rate of change.

The solution to the problem is thus Uniform.

Since the correct answer is shown in the multiple-choice option "Uniform", we conclude it matches the analysis result.