We can use the point-slope equation:
![y = mx + b](https://tex.z-dn.net/?f=y%20%3D%20mx%20%2B%20b)
m, the slope, is 3/4:
![y = \frac{3}{4} x + b](https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7B3%7D%7B4%7D%20x%20%2B%20b)
To find b, we plug in the point (4,1/3):
![( \frac{1}{3} ) = \frac{3}{4} (4) + b \\ \frac{1}{3} = 3 + b \\ \frac{1}{3} = \frac{9}{3} + b](https://tex.z-dn.net/?f=%28%20%5Cfrac%7B1%7D%7B3%7D%20%29%20%3D%20%20%5Cfrac%7B3%7D%7B4%7D%20%284%29%20%2B%20b%20%5C%5C%20%20%5Cfrac%7B1%7D%7B3%7D%20%20%3D%203%20%2B%20b%20%5C%5C%20%20%5Cfrac%7B1%7D%7B3%7D%20%3D%20%20%5Cfrac%7B9%7D%7B3%7D%20%20%2B%20b)
![- \frac{8}{3} = b](https://tex.z-dn.net/?f=%20-%20%20%5Cfrac%7B8%7D%7B3%7D%20%20%3D%20b)
Therefore, the point-slope equation is
![y = \frac{3}{4} x - \frac{8}{3}](https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7B3%7D%7B4%7D%20x%20-%20%20%5Cfrac%7B8%7D%7B3%7D%20)
Now we have to see which answer matches.
![y - \frac{3}{4} = \frac{1}{3} (x - 4) \\ y - \frac{3}{4} = \frac{1}{3} x - \frac{4}{3} \\ y - \frac{9}{12} = \frac{1}{3} x - \frac{16}{12}](https://tex.z-dn.net/?f=y%20-%20%20%5Cfrac%7B3%7D%7B4%7D%20%20%3D%20%20%5Cfrac%7B1%7D%7B3%7D%20%28x%20-%204%29%20%5C%5C%20y%20-%20%20%5Cfrac%7B3%7D%7B4%7D%20%20%3D%20%20%5Cfrac%7B1%7D%7B3%7D%20x%20-%20%20%5Cfrac%7B4%7D%7B3%7D%20%20%5C%5C%20y%20-%20%20%5Cfrac%7B9%7D%7B12%7D%20%20%3D%20%20%5Cfrac%7B1%7D%7B3%7D%20x%20-%20%20%5Cfrac%7B16%7D%7B12%7D)
![y = \frac{1}{3} x - \frac{7}{12}](https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7B1%7D%7B3%7D%20x%20-%20%20%5Cfrac%7B7%7D%7B12%7D%20)
Since this is not the same, we try the next one.
![y - \frac{1}{3} = \frac{3}{4} (x - 4) \\ y - \frac{1}{3} = \frac{3}{4} x - 3 \\ y - \frac{1}{3} = \frac{3}{4} x - \frac{9}{3}](https://tex.z-dn.net/?f=y%20-%20%20%5Cfrac%7B1%7D%7B3%7D%20%20%3D%20%20%5Cfrac%7B3%7D%7B4%7D%20%28x%20-%204%29%20%5C%5C%20y%20-%20%20%5Cfrac%7B1%7D%7B3%7D%20%20%3D%20%20%5Cfrac%7B3%7D%7B4%7D%20x%20-%203%20%5C%5C%20y%20-%20%20%5Cfrac%7B1%7D%7B3%7D%20%20%3D%20%20%5Cfrac%7B3%7D%7B4%7D%20x%20-%20%20%5Cfrac%7B9%7D%7B3%7D)
![y = \frac{3}{4} x - \frac{8}{3}](https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7B3%7D%7B4%7D%20x%20-%20%20%5Cfrac%7B8%7D%7B3%7D%20)
This is the same, so this is the answer. We should still double-check the other answers.
![y - \frac{1}{3} = 4(x - \frac{3}{4} ) \\ y - \frac{1}{3} = 4x - 3 \\ y - \frac{1}{3} = 4x - \frac{9}{3}](https://tex.z-dn.net/?f=y%20-%20%20%5Cfrac%7B1%7D%7B3%7D%20%20%3D%204%28x%20-%20%20%5Cfrac%7B3%7D%7B4%7D%20%29%20%5C%5C%20y%20-%20%20%5Cfrac%7B1%7D%7B3%7D%20%20%3D%204x%20-%203%20%5C%5C%20y%20-%20%20%5Cfrac%7B1%7D%7B3%7D%20%20%3D%204x%20-%20%20%5Cfrac%7B9%7D%7B3%7D)
![y = 4x - \frac{8}{3}](https://tex.z-dn.net/?f=y%20%3D%204x%20-%20%20%5Cfrac%7B8%7D%7B3%7D%20)
This one is not equivalent.
![y - 4 = \frac{3}{4} (x - \frac{1}{3} ) \\ y - 4 = \frac{3}{4} x - \frac{1}{4} \\ y - \frac{16}{4} = \frac{3}{4} x - \frac{1}{4}](https://tex.z-dn.net/?f=y%20-%204%20%3D%20%20%5Cfrac%7B3%7D%7B4%7D%20%28x%20-%20%20%5Cfrac%7B1%7D%7B3%7D%20%29%20%5C%5C%20y%20-%204%20%3D%20%20%5Cfrac%7B3%7D%7B4%7D%20x%20-%20%20%5Cfrac%7B1%7D%7B4%7D%20%20%5C%5C%20y%20-%20%20%5Cfrac%7B16%7D%7B4%7D%20%20%3D%20%20%5Cfrac%7B3%7D%7B4%7D%20x%20-%20%20%5Cfrac%7B1%7D%7B4%7D%20)
![y = \frac{3}{4} x + \frac{15}{4}](https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7B3%7D%7B4%7D%20x%20%2B%20%20%5Cfrac%7B15%7D%7B4%7D%20)
This one also does not work.
The answer is the second one:
The length and width are unknown.
Let the width = w.
The length is 1 more than 3 times the width.
3 times the width is 3 * w = 3w
1 more than 3 times the width is 3w + 1
We have length = 3w + 1, and width = w
The perimeter is the sum of the lengths of the 4 sides, two lengths and two widths.
P = L + L + W + W
P = 3w + 1 + 3w + 1 + w + w
Combining like terms, we get
P = 8w + 2
We are told the perimeter is 58 in., so we set our expression for the perimeter equal to 58
8w + 2 = 58
Now we solve for w, the width.
8w = 56
w = 7
The width is 7 in.
Now we solve for the length.
L = 3w + 1
L = 3(7) + 1 = 21 + 1 = 22
The length is 22 in.
The width is 7 in.
I can’t see them very well
David will finish first, because if you divide Brad's miles by 2 to his miles in a 1/4 of an hour are 5.95 miles. This means David went 6.2 miles in the same time that Brad went 5.95. Therefore, David will finish first.
This question is incomplete though as you have not listed the answers.
28.4 should be your answer as a decimal. Dividing 35 1/2 by 1 1/4 would give you 28.4.
Hope you do well though <3