y = (-1/3)x + 3 is the answer in slope intercept form
x+3y = 9 is the answer in standard form
Both forms are equivalent, just different ways to write the same thing
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Explanation:
Use the slope formula first
The points we plug in are (x1,y1) = (-3,4) and (x2,y2) = (6,1)
m = (y2-y1)/(x2-x1)
m = (1-4)/(6-(-3))
m = (1-4)/(6+3)
m = (-3)/(9)
m = -1/3
The slope of the line is -1/3
Use one of the points, say the point (x,y) = (-3,4) and the slope we just found with y = mx+b. The goal is to solve for b
y = mx+b
4 = (-1/3)*(-3) + b
4 = 1 + b
4-1 = b
3 = b
b = 3
We have m = -1/3 as the slope and b = 3 as the y intercept
Therefore, the equation in slope intercept form is y = (-1/3)x + 3
In standard form, Ax+By = C, this is is equivalent to x+3y = 9 after we multiply both sides by 3, then add x to both sides.
