Question

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

Answer 1

Answer:

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

Step-by-step 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.

$m=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}$

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

$m=\frac{1-3}{5-1}=\frac{-2}{4}=\frac{-1}{2}=\boxed{-\frac{1}{2}}$

The slope is one-half.

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

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

Our final equation is:

$y-3=-\frac{1}{2}(x-1)$