Verified answer

The slope formula you used is correct, but I'd simplify it to 1/2.

Also, since you know a point or two that the line goes through, we can just use point-slope form to make an equation.

This is of the form:

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

Where m is slope, x1 and y1 are the coordinates of any point the line passes through, and x and y remain as variables. All we do is plug in what we have. I'm going to use (2, -2) for the point, but it doesn't matter which one is chosen:

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

That's all there is to it.

There are an infinity of "equation that pass through (2,-2) and (8,1)". If you want the equation of a line, you should specify that you want the equation of a line.

Note:

Standard form of the linear equation is ax + by + c = 0

Slope-intercept form of the linear equation is y = mx+b

(y+2)/(x-2) = (1+2)/(8-2) = 3/6 = 1/2

2(y+2) = (x-2)

2y + 4 = x-2

Standard form of the equation of the line:

x - 2y - 6 = 0

Your slope is correct. = 1/2

Now use the y-intercept form to find b

y = mx + b Pick any of the two points (8,1) for example. The other one will give the same result

y = 1 and x = 8 so substitute

1 = 1/2(8) + b

solving for b gives -3

so the equation of the line you are looking for is y = 1/2x - 3

you are using the right formula, plug into y = mx + b

m = 3/6 = 1/2

y = (1/2)x + b

now plug in the initial coordinates to solve for b

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

b = -3

y = (1/2)x - 3

in standard form:

2y = x - 6

x - 2y - 6 = 0

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