Find the equation in standard form of the line with slope 5/9 that passes through the point (4, 1).

Answer 1

To adhere to Wyzant's academic integrity policy, I'm going to use an example of a similar problem to show you the techniques. It'll be up to you to use them to solve your specific problem.

Let's imagine that the slope of the line is 3/7 and that it goes through the point (-3,4). The first step would be to use this information to create a linear equation for this line. As we're given a slope and a point, the easiest form to use would be slope point form:

y-y_p=m(x-x_p)

where x_p and y_p are the x- and y-coordinates of the known point and m is the slope. For my example, the resulting equation would be

y-4 = (3/7)(x + 3)

The standard form of a linear equation is Ax + By = C where A, B, and C are whole numbers and A is positive. So, we need to do is get rid of the fraction 3/7 which is our slope. We can do this by multiplying both sides of the equation by the denominator of the slope, 7. This gives us:

7y - 28 = 3(x + 3)

Let's simplify the right side of the equation, giving us

7y - 28 = 3x + 9

In the standard form of a linear equation, the variable terms (Ax and By) are both on the same side of the equation. So let's get x and y together by subtracting 7y from both sides of the equation. The result is:

-28 = 3x - 7y + 9

In the standard form of a linear equation, the constant term (C) is by itself opposite the variable terms. So let's move 9 to the other side by subtracting 9 from both sides. This leaves us with

-37 = 3x - 7y

or

3x - 7y = -37

And there you go. We have our needed linear equation!

Answer 2

Standard form is ax + by = c.

Use point slope form for this problem:

5/9=(y-1)/(x-4)

Now manipulate this form into standard form.