Help please. Thanks in advance

Mathematics

1 answer:

anygoal [31]3 years ago

6 0

Since they want only the coordinates of the vertices. You only care about where the lines intersect, the greater than, less than signs are irrelevant.

Get each equation in 'y=mx+b' form
1) y = -x + 9
2) y = 2x-21
3) y = -4x +15

Now you can set any 2 equations equal to each other and solve for 'x'.
This will be the 'x' coordinate of the point where the 2 lines intersect.
You need 3 points, so you will need 3 different sets of 2 equations:

1) = 2)
2x -21 = -x+9
3x = 30
x = 10 -----> y = -(10)+9 = -1

1) = 3)
-x+9 = -4x+15
3x = 6
x = 2 -------> y = -(2) + 9 = 7

2) = 3)
2x - 21 = -4x+15
6x = 36
x = 6 ---------> y = 2(6) -21 = -9

Therefore the 3 intersecting points are:
(10,-1)
(2, 7)
(6, -9)

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Year: 1984 1989 1993 1997 2001 2003

Percent: 7.8 16.3 26.2 38.9 49.2 62.1

The scatter plot of the data is attached with the x-axis representing the number of years after 1980 and the y-axis representing the percent increase of donations made on behalf of a non-profit organization.

To find the equation for the line of regression where the x-axis representing the number of years after 1980 and the y-axis representing the percent increase of donations made on behalf of a non-profit organization.
$\begin{center}
\begin{tabular}{ c| c| c| c| }
 x & y & x^2 & xy \\ [1ex] 
 4 & 7.8 & 16 & 31.2 \\ 
 9 & 16.3 & 81 & 146.7 \\ 
13 & 26.2 & 169 & 340.6 \\ 
17 & 38.9 & 289 & 661.3 \\ 
21 & 49.2 & 441 & 1,033.2 \\ 
23 & 62.1 & 529 & 1,428.3 \\ [1ex]
\Sigma x=87 & \Sigma y=200.5 & \Sigma x^2=1,525 & \Sigma xy=3,641.3 
\end{tabular}
\end{center}$

Recall that the equation of the regression line is given by
$y=a+bx$
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$a= \frac{(\Sigma y)(\Sigma x^2)-(\Sigma x)(\Sigma xy)}{n(\Sigma x^2)-(\Sigma x)^2} = \frac{200.5(1,525)-87(3,641.3)}{6(1,525)-(87)^2} \\ \\ = \frac{305,762.5-316793.1}{9,150-7,569} = \frac{-11,030.6}{1,581} =-6.977$
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The graph of the regression line is attached.

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