Question

How do you find the point-slope form of the equation of the line passing through the points (–1, –3) and (4, 1)?

Answer 1

Slope equals change in `y` divided by the change in `x`
or stated equivalently
`m =(Delta y)/(Delta x)`

For this example
`m=(1-(-3))/(4-(-1)) = 4/5`

The slope point formula is
`(y - y_0) = m(x-x_0)`
and we may use either of the given points for (x_0,y_0)

Suppose we choose `(x_0,y_0) = (4,1)`

Then the slope-point formula is
`y-1 = 4/5 (x-4)`
simplifying:
`5y-5 =4x-16`
or
`5y-4x= -11`