What is the standard form of a line that passes through 31 and has a y-intercept of -2?

Answer 1

33

Answer 2

The slope intercept form of the equation of a line is y = mx + b. Since y-intercept is -2 we have

y = mx - 2 (1)

Using the point (3, 1) we can write the point-slope equation of the line such as:

(y - 1) = m(x - 3)

y - 1 = mx - 3m add 1 to both sides;

y = mx - 3m + 1 (2)

From (1) and (2) we have:

mx - 2 = mx - 3m + 1 subtract mx and 1 to both sides;

-1 - 2 = -3m

-3 = -3m divide by -3 to both sides;

1 = m

Substitute 1 for m to the equation (1):

y = mx - 2

y = x - 2 subtract x and add 2 to both sides;

y - x + 2 = 0 or

-x + y + 2 = 0 multiply by -1 to both sides;

x - y - 2 = 0 (the general form of the equation of the line, Ax + By + C = 0)