A line passes through the points (-3,-5) and (6,1). The equation of this line can be written in the form Ax + By = C, where A, B, and C are integers with greatest common divisor 1, and A is positive. Find A + B+ C.
Let's look at the two points we're given:
we can find the slope of the line by taking the difference of the respective ys, and dividing by the difference between the respective x's(rise over run). This gives us a slope of : 1 - (-5) / 6 - (-3), or (1+5) / (6+3), which is equal to 6/9 or 2/3.
With this, we can write the equation of the line as:
y = 2/3x + b. Now, we just have to solve for b, which we can find by just plugging in a point on that line. Let's use the point (6,1).
Plugging in (6,1) for the x and y values respectively, we get:
1 = 6 * 2/3 + b, or
1 = 4 + b. Subtracting 4 on both sides, we get:
-3 = b
This then gives us the equation y = 2/3x - 3, but since the question asks for standard form which is Ax + by + c = 0, we can rewrite the equation as:
3y = 2x - 9 from multiplying the equation by 3.
Then, rearranging to get our desired form, we get :
2x - 3y - 9 = 0. Since the question asks for A + B + C, we get 2 + (-3) + (-9), which is equal to 2-12, or -10