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

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

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

$\begin{gathered} m=\frac{-1-19}{-5-5} \\ m=\frac{-20}{-10} \\ m=2 \end{gathered}$

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

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