Question

Find the point-slope equation for the line that passes through the points (5,19) and (-5,-1) use the first point in your equation

Answer 1

From the question;

We are given that a line passes through the points

`(5,19),(-5,-1)`

we are to find the equation of the line using point slope equation

The point slope equation is given as

`y-y_1=m(x-x_1)`

where m is the slope.

The slope can be calculated using

`m=(y_2-y_1)/(x_2-x_1)`

From the given points

whe have the following

`\begin{gathered} x_1=5,x_2=-5 \\ y_1=19,y_2=-1 \end{gathered}`

From the values here we can find the slope

`\begin{gathered} m=(-1-19)/(-5-5) \\ m=(-20)/(-10) \\ m=2 \end{gathered}`

Hence the slope is 2

Substituting this value into the point slope intercept we have

`y-y_1=2(x-x_1)`

Inserting the values of x and y from the first point we get

The equation of the line to be

`y-19=2(x-5)`