Question

Line n passes through the points (-3, -7.5) and (2, -5). What is the equation of the line?

Answer 1

The general euqation of the line is

$y=mx+b$

where m is the slope and b tue y-intercep we can calculate each one

Slope

we use two points and the formula

$m=\frac{y2-y1}{x2-x1}$

where (x2,y2) is a right point from (x1,y1), so on this case (x2,y2) is (2,5)

now,replacing

$\begin{gathered} m=\frac{-5-(-7.5)}{2-(-3)} \\ \\ m=\frac{2.5}{5}=\frac{1}{2} \end{gathered}$

then the slope is 1/2

Y-intercept, b

we replace the value of the slope and a point, i will use (2,-5)

$\begin{gathered} y=mx+b \\ (-5)=\frac{1}{2}(2)+b \\ -5=1+b \\ \\ b=-5-1 \\ b=-6 \end{gathered}$

the y-intercept is -6

Equation of the line

replacing the slope an b

$y=\frac{1}{2}x-6$