Question

Find the equation of the line in slope-intercept form (-1,-1) and (1,0)

Answer 1

An equation in slope-intercept form of the line will be

• 
  `y\:=(1)/(2)x-(1)/(2)`

Explanation:

The slope-intercept form of the line equation

y = mx+b

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

Given the points

• (-1, -1)

• (1, 0)

Finding the slope between (-1,-1) and (1,0)

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

`\left(x_1,\:y_1\right)=\left(-1,\:-1\right),\:\left(x_2,\:y_2\right)=\left(1,\:0\right)`

`m=(0-\left(-1\right))/(1-\left(-1\right))`

`m=(1)/(2)`

substituting m = 1/2 and (-1, -1) in the slope-intercept form of the line equation to determine the y-intercept

`y = mx+b`

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

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

Add 1/2 to both sides

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

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

substituting m = 1/2 and b = -1/2 in the slope-intercept form of the line equation

`y = mx+b`

`y\:=(1)/(2)x+\left(-(1)/(2)\right)`

`y\:=(1)/(2)x-(1)/(2)`

Therefore, an equation in slope-intercept form of the line will be

• 
  `y\:=(1)/(2)x-(1)/(2)`