what's the equation for (0,2), (2,5) without a fraction?

Question

Do not use fractions in your answer

Answer 1

Hey Cindy!

 

So lets use the slope intercept form for a line:   y = mx + b

 

If we can find the slope and the y-intercept we can write the equation.

 

Well, lucky for us the y-intercept is given to us.  It's  (0,2).  So 'b' is 2.

 

Let's use the slope formula to calculate the slope.   The difference in the y coordinate over the difference in the x coordinates.    5 - 2 = 3   and  2 - 0 = 2.

So the slope of the line is   3/2  (Oh no!  A fraction!  No worries. )

So, 'm'  is  3/2

 

Substituting  2 in for 'b'  and 3/2 in for 'm'  we get the equation:

 

   y  =  3/2x  +  2

 

But we can't have any fractions in the equation! 

 Okay, so lets multiply every term on both sides by 2.  That will clear the denominator and "Poof"  no more fraction!

 

So now the equation looks like this;  2y  = 3x  +  4

 

We should probably put the equation in Standard form just keep everyone happy.

Subtract 2y from both sides.  Subtract 4 from both sides.  And switch the sides.

 

The equation will then look cool.     3x  - 2y  =  - 4

 

 

How's that?

Answer 2

Cindi, the equation for the line without fractions is to write it out in the standard form as Ax+By=C.

 

Let's start out in writing the equation in point slope form in which is:

 

y-2=(5-2)/(2-0)*(x-0)=3/2*x

 

Multiply the equation by 2 to get rid of the fraction 3/2.

 

2y-2(2)=2*(3/2)x

   2y-4 = 3x

  -2y      -2y

 

Hence, -4=3x-2y is the standard equation of the line that passes through points (0,2) and (2,5).

 

Substitute the x and y values to see if the equation is true.

 

3(0)-2(2)=-4 and 3(2)-2(5)=6-10=-4  This checks.