How do you change 2x + 3y = 7 into y – y1 = m(x-x1)? This is for a 10th grade algebra class so if you can answer it quickly, I’d be very appreciative.

Greg
Thanks

 

Greg,

The form you want has the variable y on the left side and x on the right side so I would first subtract 2x from each side.

2x + 3y = 7
3y = -2x + 7

The coefficient of y is to be 1 so divide both sides by 3

y = -2/3 x + 7/3 

If you now subtract 7/3 from each side you have an equation of the required form.

y - 7/3 =  -2/3 x, in other words
y - 7/3 =  -2/3 (x - 0)

There are other possibilities for x1 and y1, For example in the equation y = -2/3 x + 7/3 if you write  7/3 as
 9/3 - 2/3 = 3 - 2/3 then

y = -2/3 x + 7/3
y = -2/3 x + 3 - 2/3 
y = -2/3 (x - 1) + 3 
y - 3 = -2/3 (x - 1)

Penny