Question

How do you write an equation in point-slope form for the given (–1, –3) and (4, 1)?

Answer 1

Calculate the slope of a line joining the two points, then insert this slope and one of the points into the general slope-point form to give:`color(white)("XXXX")` `y-1 = 4/5(x-4)`

Explanation:

Part 1: Determine the slope
`m = (Delta y)/(Delta x) = (y_2-y_1)/(x_2-x_1)`

`color(white)("XXXX")` `= (1-(-3))/(4-(-1)) = 4/5`

Part 2: Insert this slope and point `(4,1)` into the general slope-point form
general form:
`color(white)("XXXX")` `y - haty = m(x-hatx)`

With the derived and given values
`color(white)("XXXX")` `y-1 = 4/5(x-4)`