Question

Calculate the equation on the following line

Answer 1

The equation of the line:

• 
  `y\:=\:(-3)/(2)x\:+(7)/(2)`

Explanation:

We know the slope-intercept of line equation is

`y = mx+b`

where m is the slope and b is the y-intercept

Given the points

• (3, -1)

• (-1, 5)

Finding the slope between two points (3, -1) and (-1, 5)

`\mathrm{Slope}=(y_2-y_1)/(x_2-x_1)`

`\left(x_1,\:y_1\right)=\left(3,\:-1\right),\:\left(x_2,\:y_2\right)=\left(-1,\:5\right)`

`m=(5-\left(-1\right))/(-1-3)`

`m=-(3)/(2)`

substituting m = -3/2 and the point (3, -1) in the slope-intercept form

`y = mx+b`

`-1=-(3)/(2)\left(3\right)+b`

`-(9)/(2)+b=-1`

Add 9/2 to both sides

`-(9)/(2)+b+(9)/(2)=-1+(9)/(2)`

`b=(7)/(2)`

now substituting b = 7/2 and m = -3/2 in the slope-intercept form

`y = mx+b`

`y\:=\:(-3)/(2)x\:+(7)/(2)`

Therefore, the equation of the line:

• 
  `y\:=\:(-3)/(2)x\:+(7)/(2)`