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Complete the point-slope equation of the line through (1,3) (5,1) y-3=?

User Ryryan
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1 Answer

3 votes

Answer:


\huge\boxed{y-3=-(1)/(2)(x-1)}

Explanation:

Point-slope is:


y-y_1=m(x-x_1)


m-\text{This represents the slope.}\\\\(x_1,y_1)-\text{This represents the point used in the equation.}

Our goal:

We have to complete the point-slope equation of the line through (1,3) (5,1).

--------------------------------------------------------

We have a incomplete equation of the line.


y-3=m(x-x_1)

We need to find the slope of the line, and the value of
x_1.

--------------------------------------------------------

Finding 'x1':

It seems that the value of 3 was used to be
y_1. This means that the point
(1,3) was used for the equation. This means that
x_1 would have to be 1.

Finding Slope:

Slope is rise over run.


m=(rise)/(run)=(y_2-y_1)/(x_2-x_1)

We are given the points (1,3) and (5,1).


m=(1-3)/(5-1)=(-2)/(4)=(-1)/(2)=\boxed{-(1)/(2)}

The slope is one-half.

--------------------------------------------------------

We now have enough information to complete the point-slope equation.


{\left \{ {{x_1=1} \atop {m=-(1)/(2) }} \right.}\\\\y-3=m(x-x_1)\rightarrow\boxed{y-3=-(1)/(2)(x-1)}

Our final equation is:


y-3=-(1)/(2)(x-1)

User New Moon
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