Question

How do you write an equation in standard form for the line through (1,3) and (-10,6)?

Answer 1

Start by determining the slope of the line through the given points;
then write the equation for the line in point-slope form;
finally convert to standard form.

Slope
The slope of a line is determined by the difference between 2 y-coordinate values divided by the difference between 2 corresponding x-coordinate values.
Given the points `(1,3)` and `(-10,6)`
Slope: `m = (3-6)/(1-(-10)) = - 3/11`

Point-Slope Form
The point-slope form for a line with slope `m` through a point `(y_1,x_1)` is
`(y-y_1) = m(x-x_1)`
For the given values this becomes
`y-3 = (-3/11)(x-1)`

Standard Form for Linear Equation
The standard form for a linear equation is
`Ax+By = C` (usually with the restriction that `A>=0 and Aepsilon ZZ`
`y-3 = (-3/11)(x-1)`

`y = -3/11x +3/11+3`

`3/11x+y = 36/11`

`3x+11y = 36`

(...and our work here is done)