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kolbaska11 [484]
2 years ago
13

Someone please help :')

Mathematics
1 answer:
Luden [163]2 years ago
5 0

Answer:

C. y+4=-3(x-3)

Step-by-step explanation:

The point-slope format is a way to represent the equation of a line. It involves using a point on the line and relating it to the slope in such a way that one can find any point on the line using the equation. One is asked to find the equation of a line in point-slope form. The general format for the point-slope form of a line is the following;

y-h=m(x-k)

Where the point on the line that is being used is (h,k). The parameter (m) represents the slope or rate of change in the line. The slope is often referred to as the (\frac{rise}{run}) and can be found using the following formula.

\frac{y_2-y_1}{x_2-x_1}

Where (x_1,y_1) and (x_2,y_2) are points on the line. As one can see the following points can be found on the line:

(3,-4), (0, 5)

Substitute these points into the slope formula and solve for the slope;

\frac{y_2-y_1}{x_2-x_1}

= \frac{(5)-(-4)}{(0)-(3)}

= \frac{5+4}{0-3}\\

= \frac{9}{-3}

= -3

Now substitute the slope into the given formula. As per the problem, one is supposed to use the point (3, -4) in the formula.

y-h=m(x-k)

Substitute the slope;

y-h=-3(x-k)

Substitute the point;

y+4=-3(x-3)

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a) r=\frac{4(333)-(200)(5.37)}{\sqrt{[4(12000) -(200)^2][4(9.3501) -(5.37)^2]}}=0.9857  

The correlation coefficient for this case is very near to 1 so then we can ensure that we have linear correlation between the two variables

b) m=\frac{64.5}{2000}=0.03225  

Now we can find the means for x and y like this:  

\bar x= \frac{\sum x_i}{n}=\frac{200}{4}=50  

\bar y= \frac{\sum y_i}{n}=\frac{5.37}{4}=1.3425  

b=\bar y -m \bar x=1.3425-(0.03225*50)=-0.27  

So the line would be given by:  

y=0.3225 x -0.27  

Step-by-step explanation:

Part a

The correlation coeffcient is given by this formula:

r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}  

For our case we have this:

n=4 \sum x = 200, \sum y = 5.37, \sum xy = 333, \sum x^2 =12000, \sum y^2 =9.3501  

r=\frac{4(333)-(200)(5.37)}{\sqrt{[4(12000) -(200)^2][4(9.3501) -(5.37)^2]}}=0.9857  

The correlation coefficient for this case is very near to 1 so then we can ensure that we have linear correlation between the two variables

Part b

m=\frac{S_{xy}}{S_{xx}}  

Where:  

S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}  

S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}  

With these we can find the sums:  

S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=12000-\frac{200^2}{4}=2000  

S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i){n}}=333-\frac{200*5.37}{4}=64.5  

And the slope would be:  

m=\frac{64.5}{2000}=0.03225  

Now we can find the means for x and y like this:  

\bar x= \frac{\sum x_i}{n}=\frac{200}{4}=50  

\bar y= \frac{\sum y_i}{n}=\frac{5.37}{4}=1.3425  

And we can find the intercept using this:  

b=\bar y -m \bar x=1.3425-(0.03225*50)=-0.27  

So the line would be given by:  

y=0.3225 x -0.27  

4 0
3 years ago
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