Question

Which is the slope of the line that passes through the points (3,5) and (8,7)?

Option 1: Slope = -12
Option 2: Slope = 52
Option 3: Slope = 25
Option 4: Slope = 34

Answer 1

The slope of the line passing through the points (3,5) and (8,7) is 0.4. (none of above options)

Step-by-step explanation:

To determine the slope of a line given two points, the slope formula
`\( \text{Slope} = \frac{{y_2 - y_1}}{{x_2 - x_1}} \)` is utilized. Applying this formula to the points (3,5) and (8,7):

`\( \text{Slope} = \frac{{7 - 5}}{{8 - 3}} \)`

`\( \text{Slope} = (2)/(5) \)`

`\( \text{Slope} = 0.4 \)`

The slope represents the rate of change between two points on a line. In this case, for every unit change in the x-coordinate (horizontal movement) from 3 to 8, there is a corresponding change in the y-coordinate (vertical movement) from 5 to 7. The slope of 0.4 means that for every 1 unit increase in the x-direction, there is a 0.4 unit increase in the y-direction. This indicates a positive, gentle incline on the graph, reflecting the relationship between the two points.

Hence, after calculating the slope using the coordinates (3,5) and (8,7), the accurate slope of the line passing through these points is 0.4, but not present in the options.