Math CentralQuandaries & Queries


Question from Ryan, a student:

How do you convert the equation 2x-6y=7? This is on my homework and I am really stuck!!!


You didn't tell us the form you were to convert the equation to. I am going to guess you are to convert it to point slope form, that is y = mx + b for some constants m and b. I am going to illustrate with a similar problem.

Convert the equation 8 - 3y = 15x to point slope form.

Since the point slope form has y alone on the left side of the equation I would move the constant term 8 to the right side by adding -8 to each side of the equation.

8 - 3y = 15x


8 - 3y -8 = 15x -8

and hence

-3y = 15x - 8.

All that remains is to make the coefficient of 1 rather than -6. This is accomplished by multiplying both sides of the equation by -1/3. Thus

-1/3 × (-3y) = -1/3 × (15x - 8)


y = -1/3 × 15x - (-1/3) × 8

which is

y = -5x + 8/3.

I hope this helps,

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