Question

I'm stuck on algebra.

First, write three (3) equations of lines in the following
forms: a) point-slope form, b) slope-intercept form, and c) standard form. Next, choose
another form to write each equation in, and then show all the steps required to convert each
equation to the other form.

Answer 1

point slope form : y-y1 = m(x-x1)
slope intercept form : m=(y-y1)/(x-x1)
standard form : Ax + By = C

just pick any random points on a graph and plug the same points into all three forms.

Answer 2

Algebra is tougher when they make you make up your own problems like this.

Point slope form: That's a line through point (a,b) with slope m,

y - b = m(x-a)

Let's pick point (2,-3) and slope 7,

y + 3 = 7(x-2)

Slope-intercept form: That's a line given slope m and y intercept b,

y = mx + b

We'll pick slope m=3 and y intercept -2:

y = 3x - 2

Standard form: That's ax+by=c or sometimes ax+by+c=0; standard form isn't standard. We'll go with the former, picking some random numbers for a,b,c;

4x - 3y = 5

Let's write all three equations in all three forms

y + 3 = 7(x-2) point/slope

y = 7x - 14 - 3

y = 7x - 17 slope/intercept

7x - y = 17 standard

~~~~~~~~~~

y = 3x - 2 slope/intercept

y + 2 = 3x point/slope

3x - y = 2 standard

~~~~~~~~~~~~~~~

4x - 3y = 5 standard

3y = 4x - 5

y = (4/3) x - (5/3) slope/intercept

y + 5/3 = (4/3) x point/slope