Homework Help

How do you change the form of a linear function from standard to point-slope and vice...

user profile pic

hngould17 | eNoter

Posted August 15, 2012 at 10:42 PM via web

dislike 0 like

How do you change the form of a linear function from standard to point-slope and vice versa?

2 Answers | Add Yours

user profile pic

embizze | High School Teacher | (Level 1) Educator Emeritus

Posted August 15, 2012 at 11:05 PM (Answer #1)

dislike 1 like

The standard form of a linear equation is Ax+By+C=0.

The point slope form of a linear equation: given a point `(x_1,y_1)` and a slope `m` the equation is `y-y_1=m(x-x_1)`

The slopeintercept form is `y=mx+b` where m is the slope and b the y-intercept.

(1) If you are given the standard form, if you solve for y you will have the slope-intercept form.

`Ax+By+C=0`

`By=-Ax-C`

`y=-A/Bx-C/B` where `m=-A/B` and the y-intercept `b=-C/B`

If you are asked to write in point-slope form (and this shouldn't happen) then you can find teh slope (`m=-A/B` ), and you will have to find a point that lies on the line. (My choice would be to substitute x=0 to get the y-intercept) then use `y-y_1=m(x-x_1)` where the point you found was `(x_1,y_1)` .

(2) Given point-slope form:

Again solve for y; this is easier with an example. Given (1,2) and m=3 you have `y-2=3(x-1)`

Solve for y to get `y-2=3x-3==>y=3x-1`

This is slope-intercept form.

To put into standard form we need everything on one side:

`3x-y-1=0`

** Note that there is more than 1 correct "standard form"

Given 3x-y-1=0 these are the same line:

-3x+y+1=0

6x-2y-2=0

etc...

Sources:

user profile pic

Wiggin42 | TA , Grade 11 | Valedictorian

Posted April 27, 2014 at 1:22 AM (Answer #2)

dislike 0 like

Standard form is: Ax + By + C where A,B, and C are non-zero integer coefficients. 

Point slope form is: y - y1 = m(x - x1) where m is the slope and (x1, y1) is a point. 

Lets give an easy example to show how to go between the two forms: 

-10x + 2y = 20

-5x + y = 10

y = 5x + 10    (This is slope-intercept form.)

y = 5(x + 2)  (Pull out the slope)

And there you have point-slope form!

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes