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=(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=(-5-(-7.5))/(2-(-3)) \\ \\ m=(2.5)/(5)=(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)=(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=(1)/(2)x-6`