Question

Write the equation of the line that passes through the points (3,-2) and (5, -1).

Answer 1

The equation of the line that passes through points (3 , -2) and (5 , -1)

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

Step-by-step explanation:

The equation of a line in point slope form is:

$y-y_{1}=m(x-x_{1})$, where m is the lope of the line and $(x_{1},y_{1})$

are the coordinates of a point lies on the line

The slope of a line that contains points $(x_{1},y_{1})$ and $(x_{2},y_{2})$ is

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Write the equation:

1. That passes through the points (3 , -2) and (5 , -1)

2. Put your answer in fully reduced point-slope form

Let point (3 , -2) = $(x_{1},y_{1})$ and point (5 , -1) = $(x_{2},y_{2})$

∵ $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

∴ $m=\frac{-1-(-2)}{5-3}=\frac{-1+2}{2}=\frac{1}{2}$

∵ The equation of the line is $y-y_{1}=m(x-x_{1})$

∵ $(x_{1},y_{1})$ = (3 , -2)

∵ m = $\frac{1}{2}$

- Substitute the coordinates of the point and m in the equation

∴ $y-(-2)=\frac{1}{2}(x-3)$

∴ $y+2=\frac{1}{2}(x-3)$

The equation of the line that passes through points (3 , -2) and (5 , -1)

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

Learn more:

You can learn more about equation the line in brainly.com/question/12967961

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