Hi Ken,

The y-intercept form or sometimes called the slope intercept form of a line is

y = (a number) x + (a number)

for example y = 2x + 5 or y = 8x - 1.

If you have an equation of a line, say for example 5x + 3y -2 = 0, then you can convert it into the
y-intercept form as follows. First I want the y term on the left of the equal sign and the x term and the constant term on the right side. To accomplish this I add -5x to both sides to get

 

5x + 3y - 2 - 5x= - 5x or 3y - 2 = -5x

and then I add 2 to both sides to get

3y - 2 + 2 = -5x + 2 or 3y = -5x + 2

All that remains is to change the coefficient of y from 3 to 1. This I can do by dividing both sides by 3.

3y/3 = (-5x + 2)/3
y =  ^-5/₃ x +  ²/₃

This is the equation of the line 5x + 3y -2 = 0 in y-intercept form.

For your second question I don't know what you mean by standard form.

Penny