Question

How would I figure out a linear equation with two plot points with fractions? (1/3(6),3) and (1/2(19),-2) are my two plot points. I was able to graph them on Desmos, but I can't seem to figure out how I would go about figuring out the slope and y-intercept in this case... the fractions are what's throwing me off here. Please help!

Answer 1

Answer:
`m=(-30)/(79),\ y=5.40`

Explanation:

Given

Points are
`\left(6(1)/(3),3\right),\ \left(19(1)/(2),-2\right)`

Convert mixed numeral to fraction

`\left(6(1)/(3),3\right)\Rightarrow \left((19)/(3),3\right)\\\\\left(19(1)/(2),-2\right)\Rightarrow \left((39)/(2),-2\right)`

Slope of the line is

`\Rightarrow m=(3-(-2))/((19)/(3)-(39)/(2))\\\\\Rightarrow m=(5)/((38-117)/(6))\\\\\Rightarrow m=(-30)/(79)`

Equation of line

`\Rightarrow (y-3)/(x-(19)/(3))=(-30)/(79)\\\\\text{for y-intercept, put x=0}\\\\\Rightarrow (y-3)/(0-(19)/(3))=(-30)/(79)\\\\\Rightarrow y-3=(190)/(79)\\\\\Rightarrow y=3+2.40\\\Rightarrow y=5.40`