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kap26 [50]
1 year ago
11

Karen recorded her walking pace in the table below. what equation best represents this relationship

Mathematics
1 answer:
REY [17]1 year ago
8 0

Given Data:

The table given here shows time taken in the first column and the distance travelled in the second column.

First check the ration of distance /time to verify if the speed of the man is constant or not.

\begin{gathered} \frac{8.75\text{ m}}{2.5\text{ h}}=3.5\text{ m/h} \\ \frac{14\text{ m}}{4\text{ h}}=3.5\text{ m/h} \end{gathered}

As both ratios are same it means the speed of the man is constant and the distance travelled is directly proportional to the time taken and varies linealy with the time.

Now to determine the relationship between <em>m</em> and <em>h </em>we will use the same ratio of <em>m</em> and <em>h</em> which comes in the previous step.

\begin{gathered} \frac{m}{h}=3.5 \\ m=3.5h \end{gathered}

Thus, option (D) is the required solution.

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Step-by-step explanation:

We can take any two input-output pairs from the table to find the equation of given function.

Linear function is given by:

y =mx+b

Here m is the gradient of the functions which is defined as:

m = \frac{rise}{run} = \frac{y_2-y_1}{x_2-x_1}

The input-output pairs are:

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First of all,

m = \frac{-4-(-1)}{0-(-1)}\\= \frac{-4+1}{1} = -3

Putting the value of slope in the equation

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Putting (-1,-1) in the equation

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The equation will be:

y = -3x-4

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Equation: y = -3x-4

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