Question

Point slope form and standard form

Answer 1

The point slope form, , is useful in situations involving slope and the location of one or more points. The standard form, , is usually easier to use when we need to make algebraic calculations. When needs or knowledge change, we can convert an equation from one form into another.

Answer 2

The slope-intercept form (not asked for) is the y=mx+b form, where m is the slope and b is the y-value of the y-intercept (0,b).
This form only works if you have both the slope and y-intercept.

If you have the slope and some other point on the line, say (x1, y1), then the point slope form is:
y - y1 = m ( x - x1 )

So, if you have a slope of 7 and a point (2, -6), then your point-slope form would be:
y - (-6) = 7 ( x- 2) or y+6=7(x-2)

Now standard form is the Ax+By=C format. You can turn any slope-intercept equation or point-slope equation into that form by distributing everything out and getting the x’s and y’s to the left side. Often you’ll also make sure you don’t have any fractions.

Taking the last answer I had, y+6=7(x-2), I’d put this into standard form by distributing:
y+6=7(x-2)

y+6 = 7x - 14

Then move 7x to the left by subtracting and move 6 to the right by subtracting:

-7x + y = -20