With a slope of -1/4 through (2,2)

Question

How do you solve with a fraction?? And write in standard form???

Answer 1

You would do it exactly the same way as if it were not a fraction!

Recall that we know 3 forms of the equation of the line:

1. The standard form Ax+By=C where A,B, C are integers and A is positive or 0;
2. The slope-intercept form: y=mx+b where m is the slope and b is the y intercept; and
3. The point-slope form: y-y0=m(x-x0) where m is the slope and (x0,y0) is the point.

So in your case you know the slope m=-1/4 and the point is (x0,y0)=(2,2). So examining the three options, you should start with what you are given ie the point slope form. This gives you y-2=-1/4 *(x-2)

Now we have to turn this into the standard form. While there are several ways to do this, the method I found to lead to fewest arithmetic or algebra mistakes is as follows

1. Find all the denominators and multiply the equation by them. In this case, we have a denominator of 4 so we multiply by that to get 4(y-2)=4*-1/4*(x-2)
2. Simplify and open the brackets. Note here that 4*-1/4=-1 and so we get 4(y-2)=-1(x-2) or after opening the brackets 4y-8=-x+2.
3. Now move the x and y to one side, keeping the x positive and the numbers to the opposite. 4y+x=10

Answer 2

Use the Point-Slope Form for the equation of a line: y - y₁ = m(x - x₁).

y - 2 = (-1/4)(x - 2)

y - 2 = (-1/4)x + 1/2

Multiply both sides of the equation by 4 to eliminate the fractions.

4y - 8 = -x + 2

x + 4y = 10