Equations of a Line

Rewriting an Equation of a Line

Equation of a Line

• There are 3 ways to write an equation of a line.

  •Slope-Intercept Form y=mx+b

  •Point-Slope Form y-y1=m(x-x1 )

  •Standard Form Ax+By=C

  
  

• They are the same equation, just written differently.

Let’s Practice

Write the equation in standard form.
- Go from y=mx+b form to Ax+By=C
- No fractions in final answer! 

 $y=4x-18$                                               $y=2x+\frac{3}{7}$ 



 

Multiple Choice

Write the equation in standard form.

$$y=-\frac{1}{2}x-10$$  

• $$2x+2y=20$$  

• $$2x+y=20$$  

• $$2x+2y=-20$$  

• $$x+2y=-20$$  

Multiple Choice

Write the equation in standard form.

$$y=\frac{1}{3}x+2$$  

• $$-x+3y=6$$  

• $$3x+y=6$$  

• $$x+3y=6$$  

• $$3x-y=6$$  

Let's Practice

Write an equation going from point-slope form  $y-y1=m\left(x-x1\right)$  to standard form  $Ax+By=C$  .

 $y-2=\frac{1}{2}\left(x+1\right)\ \$                               $y+3=\frac{2}{3}\left(x-6\right)$  

Multiple Choice

Write the equation in standard form.

$$y-1=\frac{2}{3}\left(x+6\right)$$  

• $$3x-2y=-15$$  

• $$2x-3y=-15$$  

• $$2x+3y=15$$  

• $$3x+2y=15$$