Question

determine the equation of the line that passes through the following points (-2 1/4, 1 3/4) and (-3, 3)​

Answer 1

`y=-(5)/(3)x-2`

Explanation:

step 1

Convert mixed number to an improper fraction

`-2(1)/(4) =-2-(1)/(4)=-(9)/(4)`

`1(3)/(4) =1+(3)/(4)=(7)/(4)`

so

we have the points

`(-(9)/(4),(7)/(4))` and
`(-3,3)`

step 2

Find the slope of the line

The formula to calculate the slope between two points is equal to

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

we have the points

`(-(9)/(4),(7)/(4))` and
`(-3,3)`

substitute

`m=(3-(7/4))/(-3+(9/4))`

`m=(5/4)/(-3/4)`

`m=-(5)/(3)`

step 3

Find the equation of the line in point slope form

`y-y1=m(x-x1)`

we have

`m=-(5)/(3)`

`point\ (-3,3)`

substitute

`y-3=-(5)/(3)(x+3)`

step 4

Convert to slope intercept form

Isolate the variable y

`y-3=-(5)/(3)x-5`

`y=-(5)/(3)x-5+3`

`y=-(5)/(3)x-2`