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 9/4.
(Simplify your answer.)
Which graph represents this relationship?
A.
B.
C.
Which graph represents this relationship?
Share
To find the slope of the line through the points (4,9) and (16,36), we use the formula for 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) ).
Now, plug in the values:
[
m = frac{36 – 9}{16 – 4} = frac{27}{12}
]
Next, simplify ( frac{27}{12} ):
[
m = frac{9}{4}
]
Now that we have the slope ( frac{9}{4} ), you can use this to graph the line. You can choose a point and use the slope to find another point. Starting at (4, 9), moving up 9 units and right 4 units (as the slope indicates), you can find additional points on the line.
To determine which graph represents this relationship, look for a line passing through the points (4, 9) and (16, 36) with a slope of ( frac{9}{4} ). The correct graph should show an increasing line with the appropriate steepness.
If you have specific graphs A, B, and C available, please