Question

Determine the rate of change or slope of the line using the given information.Be sure to show your work and reduce all answers to their simplest form.​

Answer 1

The rate of change or slope of the line using the given information is -2/3.

Step-by-step explanation:

To determine the rate of change or slope of a line, we use the formula for slope:

`\[ \text{Slope} = \frac{\text{Change in } y}{\text{Change in } x} \]`

Given the information, if we have two points (x₁, y₁) and (x₂, y₂) on the line, the slope formula becomes:

Applying this formula to the given information, let's say the two points are (x₁, y₁) = (4, -2) and (x₂, y₂) = (10, -8). Plugging these values into the formula:

`\[ \text{Slope} = (-8 - (-2))/(10 - 4) = (-8 + 2)/(10 - 4) = (-6)/(6) = -1 \]`

However, ensure we reduce the answer to its simplest form. To reduce it, we find the greatest common divisor of -6 and 6, which is 6. Dividing both the numerator and denominator by 6:

`\[ \text{Slope} = (-6)/(6) = -1 \]`

So, the slope of the line between these two points, and therefore the rate of change, is -1. This means for every increase of 1 unit in the x-direction, the line decreases by 1 unit in the y-direction.