Question

explain how to find the equation of the line, in standard form and slope–intercept form, passing through (3, 6) and (–2, –4)

Compare the benefits of writing an equation in standard form to the benefits of writing an equation in slope–intercept form

Answer 1

Standart form is:
Ax+By=C
in this form (A,B) is the perpendicular vector to the line.
to find it first find the direction vector of the line: (-2-3,-4-6)=(-5,-10) which is same direction as (-1,-2) which is more simple, :). Now find perpendicular vector to it . (2,-1) will do. Put the coordinates of the point (3,6) and this perpedicular vector into Ax+By=C:
2(x-3)-1(y-6)=0
reorganizing a bit: 2x-y=0 is the equation in standart form.

Slope-intercept form:
y=mx+b, where m is the slope and b y-intercept.
to find m take the ratio of the direction vector. -2/-1=2
put coordinates of the point: y-6=2(x-3) and reorganizing:
y=2x is your equation

Answer 2

@Tati_Lee