Question

Write an equation in slope intercept form for the line that passes through (-1, -2) and (3, 4)

Answer 1

The slope-intercept form of the line equation is:

• 
  `y=\:(3)/(2)x\:-(1)/(2)`

Explanation:

The slope-intercept form of the line equation

y = mx+b

where

• m is the slope

• b is the y-intercept

Given the points

• (-1, -2)

• (3, 4)

Determining the slope between (-1, -2) and (3, 4)

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

`\left(x_1,\:y_1\right)=\left(-1,\:-2\right),\:\left(x_2,\:y_2\right)=\left(3,\:4\right)`

`m=(4-\left(-2\right))/(3-\left(-1\right))`

`m=(3)/(2)`

Thus, the slope of the line is:

m = 3/2

substituting m = 3/2 and the point (3, 4) in the slope-intercept form of the line equation

y = mx+b

`4=(3)/(2)\left(3\right)+b`

switch sides

`(3)/(2)\left(3\right)+b=4`

`(9)/(2)+b=4`

subtract 9/2 from both sides

`(9)/(2)+b-(9)/(2)=4-(9)/(2)`

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

now substituting m = 3/2 and b = -1/2 in the slope-intercept form of the line equation

`y = mx+b`

`y=\:(3)/(2)x\:+\:\left(-(1)/(2)\right)`

`y=\:(3)/(2)x\:-(1)/(2)`

Therefore, the slope-intercept form of the line equation is:

• 
  `y=\:(3)/(2)x\:-(1)/(2)`