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QuestionFind the slope of the line for the points (1,10) to (2,20) and for (1,10) to (5,50). What does it represent?

Studdy Solution

STEP 1

Assumptions1. The points on the graph are (1,10), (,20), (3,30), (4,40), (5,50) . The x-axis represents time (in hours)
3. The y-axis represents distance (in miles)
4. The slope of the line represents the rate of change of distance with respect to time

STEP 2

First, we need to find the slope of the line for the first two hours. The slope of a line is given by the change in y divided by the change in x.
lope=ΔyΔxlope = \frac{\Delta y}{\Delta x}

STEP 3

Now, plug in the given values for the first two points to calculate the slope.
lope=20−102−1lope = \frac{20 -10}{2 -1}

STEP 4

Calculate the slope for the first two hours.
lope=20−102−1=10lope = \frac{20 -10}{2 -1} =10

STEP 5

Next, we need to find the slope of the line for all five hours. Again, the slope of a line is given by the change in y divided by the change in x.
lope=ΔyΔxlope = \frac{\Delta y}{\Delta x}

STEP 6

Now, plug in the given values for the first and last points to calculate the slope.
lope=50−105−1lope = \frac{50 -10}{5 -1}

STEP 7

Calculate the slope for all five hours.
lope=50−105−1=10lope = \frac{50 -10}{5 -1} =10

STEP 8

The slope of the line represents the rate of change of distance with respect to time. In this case, it represents the speed at which Akio is biking. The slope for the first two hours and for all five hours is the same, which means that Akio is biking at a constant speed of10 miles per hour.
The slope of the line for the first two hours is10 miles per hour. The slope of the line for all five hours is also10 miles per hour. This means that Akio is biking at a constant speed of10 miles per hour.

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