The points (4, 9) and (16, 36) form a proportional relationship. Find the slope of the line through the points. Then use the slope to graph the line.
The slope is __. (Simplify your answer.)
What is the slope of the line through the points (4, 9) and (16, 36) and how do you graph the line using the slope?
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To find the slope of the line that passes through the points (4, 9) and (16, 36), we can use the formula for the slope ( m ):
[
m = frac{y_2 – y_1}{x_2 – x_1}
]
Here, ( (x_1, y_1) = (4, 9) ) and ( (x_2, y_2) = (16, 36) ).
First, we substitute the values into the formula:
[
m = frac{36 – 9}{16 – 4} = frac{27}{12}
]
Now, we simplify ( frac{27}{12} ):
[
m = frac{9}{4}
]
So, the slope of the line is ( frac{9}{4} ).
### Explanation:
The slope represents the rate of change between the y-values and the corresponding x-values of the points. Simplifying ( frac{27}{12} ) gives us ( frac{9}{4} ), making it easier to interpret and use for graphing.
To graph the line, you can start at the point (4, 9) and use the slope ( frac{9}{4} ) to find additional points. This means that for every 4 units you move to the right (increase in x), you move up