Question

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

Answer 1

`\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).

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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`.

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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.

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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)`