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Roman55 [17]
3 years ago
6

1). Write an equation of a line with the given slope and y-intercept.

Mathematics
1 answer:
asambeis [7]3 years ago
4 0

Answers:



1) The Equation of a Line is:


y=mx+b    (1)


Where:


m is the slope


b is the y-intercept



For this problem we have a given m=-2 and a given b=4


So, we only have to substitute this values in the equation (1):


y=-2x+4    


This is option B



2) Here we have to find the slope m and the y-intercept b of this equation:


y=\frac{1}{5}x-8    


According to the explanation in the first answer related to the equation (1), the slope of this line is:


m=\frac{1}{5}


And its y-intercept is:


b=-8


This is option C



3) We have to Equations of the Line, and we are asked if these are parallel:


y=6x+9    (a)


27x-3y=-81    (b)



Equation (b) has to be written in the same form of (a), in the form y=mx+b in order to be able to compare both:


-3y=-81-27x    


y=-\frac{1}{3}(-81-27x)    


y=\frac{81}{3}+\frac{27}{3}x    


y=9x+27    (c)



There is a rule that establishes that <em><u>Two lines are parallel if they have the same slope</u></em>. In this case, if we compare equations (a) and (c) we find they don’t have the same slope, then <u>they are not parallel</u>.


4) Here we are asked to write y=\frac{3}{5}x+4 in a standard form with integers:


-\frac{3}{5}x+y=4


Multiply each side by 5:


5(-\frac{3}{5}x+y)=5(4)


5(-\frac{3}{5}x)+5y=20


-3x+5y=20


In this case none of the options apply, please check if the question was written correctly.


5) In this question we are asked to write an equation parallel to:


y=2x+7     (2)


That passes through the given point (3,11). <u>(Notice that in the Cartesian plane the points have an x-component and a y-component)</u>

First, remember that <u>two Equations of the line are parallel when they have the same slope</u>. Now that this is clear, we are going to use the equation of the slope with the given point to find the parallel equation:


Equation of the slope:


m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}    (3)


From (2) we know the slope is 2, then we only have to substitute this value and the points in (3):


2=\frac{y-11}{x-3}    

2(x-3)=y-11      

2x-6=y-11      

Finally:


y=2x+5      

This is option B



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