Question

How do you rewrite an equation from point-slope form to slope-intercept form? And from slope-intercept form, how do you convert to standard form?

Answer 1

If I remember it properly point-slope for is in terms of x= and slope-intercept form is in terms of y=

Answer 2

Begin by writing an equation in point slope form: (y - y1) = m(x - x1). Then manipulate it until you have the form y = mx + b. Then, go a step further and manipulate it until you have the form ax + by = c

For example, suppose you're given the point (x,y) = (2,5) and the slope m = 3. Rewriting this in point slope form produces:

(y - 2) = 3( x -5) .

To re-write this equation in slope-intercept form, manipulate the equation as follows:

(y - 2) = 3(x - 5)
y - 2 = 3x - 15
y = 3x - 15 + 2
y = 3x - 13

This last form, y = 3x - 13 is the slope-intercept form y = mx + b.

Finally, to put this equation in standard form ax + by = c, manipulate the equation as follows:

y = 3x - 13
13 = 3x - y
13 = 3x - 1y
3x + (-1)y = 13
The last form, 3x + (-1)y = 13 is the standard form ax + by = c.