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Aleksandr-060686 [28]
3 years ago
5

A line passes through the points (6,5) and (2,2) . Select Yes or No to tell whether each equation describes this line. Equation

Yes No y−5=34(x−6) y−5=−43(x−2) y−2=−34(x−6) ​y−2=34(x−2)​
Mathematics
1 answer:
Marta_Voda [28]3 years ago
3 0

ANSWER

y-5=\frac{3}{4}(x-6),Yes

y-5=-\frac{4}{3} (x-2),NO

y-2=-\frac{3}{4} (x-6),NO

y-2=\frac{3}{4}(x-2),Yes


EXPLANATION

The line passes through these two points, (6,5) and(2,2).


We can use these two points to determine the slope of the line.

The formula for finding the slope of a line when at least two points are known is m=\frac{y_2-y_1}{x_2-x_1}.


We can choose (x_1,y_1)=(6,5) and (x_2,y_2)=(2,2) or (x_1,y_1)=(2,2) and (x_2,y_2)=(6,5).


We shall get the same result.


m=\frac{2-5}{2-6} =\frac{-3}{-4} =\frac{3}{4}.


We now determine the equation of the line using the poit-slope formula,


y-y_1=m(x-x_1).


When we choose (x_1,y_1)=(6,5), then we will obtain,


y-5=\frac{3}{4}(x-6) as the point-slope form.


When we choose (x_1,y_1)=(2,2), then we will obtain,


y-2=\frac{3}{4}(x-2) as the point-slope form.

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