Question

What is the equation of the line passingt through the points (2/5,19/20) and (1/3,11/12) in slope-intercept form?

Answer 1

the answer to the question

Answer 2

Answer: The required equation of the line in slope-intercept form is
`y=(1)/(2)x+(3)/(4).`

Step-by-step explanation: We are given to find the equation of the line passing through the points
`\left((2)/(5),(19)/(20)\right)` and
`\left((1)/(3),(11)/(12)\right)` in slope-intercept form.

We know that

the slope of a line passing through the points (a, b) and (c, d) is given by

`m=(d-b)/(c-a).`

So, the slope of the given line will be

`m=((11)/(12)-(19)/(20))/((1)/(3)-(2)/(5))=((55-57)/(60))/((5-6)/(15))=(-2)/(60)*(15)/(-1)=(1)/(2).`

Also, since the line passes through the point
`\left((2)/(5),(19)/(20)\right)`, so its equation will be

`y-(11)/(12)=m\left(x-(1)/(3)\right)\\\\\\\Rightarrow y-(11)/(12)=(1)/(2)\left(x-(1)/(3)\right)\\\\\\\Rightarrow y=(1)/(2)x-(1)/(6)+(11)/(12)\\\\\\\Rightarrow y=(1)/(2)x+(11-2)/(12)\\\\\\\Rightarrow y=(1)/(2)x+(3)/(4).`

Thus, the required equation of the line in slope-intercept form is
`y=(1)/(2)x+(3)/(4).`