Question

Based on the line of best fit, which of these would be the best prediction for the number of cars washed in Week 10?

Answer 1

http://assets.openstudy.com/updates/attachments/4fe29330e4b06e92b8717d8f-rainbow.ninja-1340248893921-04_11_91.jpg

Answer 2

Since they've already drawn the line of best fit, we don't have to figure it out, which makes our solution a little easier. All we need to do is figure out the equation of that line, and then we could plug in 10 for the x value and get our y value, which will be our answer.

It's seen that the y intercept is 0, so the line will be of the form y=mx. We can solve for the slope by remembering that
\[slope=m=(\Delta y)/(\Delta x)\]

So we can pick any point on the line of best fit and find the slope between that point and the point (0,0). Lets use the point (4,10). The change in y of these two points is 10 and the change in x is 4. So the slope is 10/4 or 2.5. The equation for the line of best fit is therefore
\[y=2.5x\]

Plug in 10 for x and you get 25 cars.

Answer 3

thank you so much :) Choose the slope-intercept equation of the line that passes through the point (6, 4) and is parallel to y = 1/3 x - 3. @vinnv226

Answer 4

For two lines to be parallel, they must have the same slope. So, in this example, our answer will have a slope of 1/3. Since you have the slope and a point, you can now plug into the slope-intercept equation, which is:
\[y-y_1=m(x-x_1)\]

If you'd like help plugging in or simplifying let me know.

Answer 5

Sorry to bother you, but i do need help-.- @vinnv226

Answer 6

Ok. Our "m" is our slope, which as mentioned is equal to 1/3. The x_1 and y_1 are the coordinates of any point on the line. We know (6,4) is on the line, so our x_1 will be 6 and our y_1 will be 4. Plugging all these in, we get:
\[y-4=(1/3)(x-6)\] Distributing our 1/3 we get:
\[y-4=(x/3)-2\] Add 4 to both sides and we're finished:
\[y=(x/3)+2\]