Rate of Change Problem #1 [Algebra]

Rate of Change Problem #1:

Find the rate of change for each table below. Explain what the rate of change means for each situation.

Rate of change problem #1


Answer:

For the rate of change problem #1, we can use the slope or rate of change formula.

$$slope=\frac{rise}{run}$$

$$slope=\frac{y_{2}-y_{1}}{x_{2}-x{1}}$$

Let’s use the two coordinates first: (4,232) and (6,348). We would have to plug these coordinates to the slope formula.

$$slope=\frac{348-232}{6-4}$$
$$slope=\frac{116}{2}$$
$$slope=58$$

Let’s use another pair of coordinates to confirm if the slope is constant. Let’s use (8,464) and (10,580) in the slope formula again.

$$slope=\frac{580-464}{10-8}$$
$$slope=\frac{116}{2}$$
$$slope=58$$

If we use the same formula for the pairs (6, 348) and (8, 464), the slope would be the same.

$$slope=\frac{464-348}{8-6}$$
$$slope=\frac{116}{2}$$
$$slope=58$$

Comparing the slopes or rate of change, we could deduce that the rate of change is constant at 58 miles per hour.


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