Hello Everyone,o I just have one math question that I am stuck on because it has so many parts. Any sort of help would be highly appreciated. Thanks to everyone contributing. Once again, thanks so much! :)
Heres the question:
A linear model for the data in the table is shown in the scatter plot.
x values: 1, 2, 4, 5, 6, 7, 8, 9
y values: 14, 12, 11, 11, 9, 7, 4. 3.5
VIsual:
| x | 1 | 2 | 4 | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|---|---|---|
| y | 14 | 12 | 11 | 11 | 9 | 7 | 4 | 3.5 |
Which two points should you use to find the equation of the model? Explain.
Use the two points you chose in Part (a) to find the slope of the linear model, rounded to three decimal places. Show your work.
What is the equation of the linear model in point-slope form?
Rearrange the equation you wrote in Part (c) into slope-intercept form. Show your work.
+998 Okay, let's solve this one.
I would personally choose the coordinates \((1 , 14)\) and \((2 , 12)\), because they are going to make my life much easier than using coordinates that have decimals in them. Therefore, when we find the slope, we have zero rounding to do.
Now, we are going to use the formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\) to find the slope, \(m\).
Plugging in our numbers, we get \(m = \frac{12 - 14}{2 - 1}\), which is equal to \(\boxed{-2}\).
+998 So we know that our slope is \(-2\).
Point slope form is in the form of \((y-y_1) = m(x - x_1)\).
Using our coordinate (I'm going to choose \((1 , 14)\) ), and plugging it into the formula, we get our point-slope form to be
\(\boxed{y-14 = -2(x-1)}\).
+998 Now for the final part, we need to rearrange the eqution: \({y-14 = -2(x-1)}\) into slope-intercept form.
Slope-intercept form is in the form of \(y = mx + b\).
Rearranging our equation to look like this, we get:
\({y-14 = -2(x-1)}\),
\(y = -2(x-1) + 14\),
\(y = -2x + 2 + 14\)
\(y = -2x + 16\).
Therefore, our answer is \(\boxed{y = -2x + 16}\).
We can test this by inserting an ordered pair, let's say \((2,12)\).
\(12 = -4 + 16\),
\(12 = 12\)
Is this equation true? YES!!!!.. This tells us that our answer is correct!
