Question

Write the equation of the line that passes through the points (3,5) and (6,2), giventhat the point slope form is y 3 - 10.30 - 5), in slope-intercept form.

Answer 1

`\begin{gathered} (3,5) \\ (6,2) \end{gathered}`

the general equatin of a line is

`y=mx+b`

where m is the slope and b the y-intercept

firs find the slope using

`m=(y2-y1)/(x2-x1)`

where (x2,y2) is a right point from (x1,y1)

on this case (x2,y2) is (6,2)

so replacing

`\begin{gathered} m=(2-5)/(6-3) \\ \\ m=(-3)/(3)=-1 \end{gathered}`

the slope is one

now to calculate b we replace the slope and a point and solve b

i will use (3,5)

`\begin{gathered} (5)=(-1)(3)+b \\ 5=-3+b \\ b=5+3 \\ b=8 \end{gathered}`

now replacing the slope and b, the equation of the line is

`y=-x+8`