Question

How do you write an equation in standard form given a line that passes through (-9,-2) and (7,9)?

Answer 1

The easiest way to solve this requirement is to:

• Step 1: write the equation in point-slope form
• Step 2: convert the point-slope form into standard form

Step1: point-slope form
Given the two points `(-9,-2)` and `(7,9)`
the slope is given as
`color(white)("XXXXX")` `m=(Delta y)/(Delta x) = (9-(-2))/(7-(-9)) = 11/16`
Using this slope and the point `(7,9)` (we could use either given point)
the point-slope form is
`color(white)("XXXXX")` `(y-9) = 11/16(x-7)`

Step 2: Convert to standard form
Standard form is (normally) expressed as
`color(white)("XXXXX")` `Ax+By=C` with `A>=0 and AepsilonZZ`
Starting with
`color(white)("XXXXX")` `(y-9) = 11/16(x-7)`
we can write
`color(white)("XXXXX")` `16(y-9) = 11(x-7)`

`color(white)("XXXXX")` `16y - 144 = 11x -77`

`11x -16y = -67` `color(white)("XXXXX")`(standard form)