Write an equation of the line, in standard form, given the slope is -1/3 and the point (5,-2) is on the line.

Question

I need help on this because I can't write in standard form. Thank You for the help.

Answer 1

Standard form look like this Ax + By = C.

1st step use the point slope formula because you are given a point and a slope.

(y - y1) = m(x - x1)

(y - -2) = -1/3 (x - 5)

y + 2 = -1/3x + 5/3

y = -1/3x - 1/3

Now change it to standard form:

1/3x + y = -1/3

Note you don't want fractions in the formula so multiply by three to get rid of the fraction.

x + 3y = -1

Let me know if this helped you or if you need more help.

Answer 2

The equation of a line is on the form of Ax + By = C. For this problem, it's easier to write the slope equation (since we have the slope) and then get the line equation from it. The slope equation is y = mx + b.

If you look at the slove equation you can see that we have values for x and y which are (5, -2) and we have value for m which is -1/3, so the only unknow value is b. If we plug in all those known values, we can solve for b. Let's do it!

y = mx + b

First step, we plug in the value for the slope, m

y = (-1/3)x + b

Then we plug in the values for (x, y)

-2 = (-1/3)5 + b

-2 = -5/3 + b

b = -2 + 5/3

which gives us b = -1/3

So now, since we have the value for b we can write the slope equation.

y = mx + b (we only have to plug in m and b)

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

y = -x/3 - 1/3

To make the equation simpler, we multiply all terms by 3, that way we get rid of the fractions (nobody likes fractions anyway).

3y = - x - 1

For the equation of the line you want x and y terms to be on the same side, so we add +x in both terms, we get

x + 3y = - 1

And we're done.