Answer:
2x-3y=9
Explanation:
To find the equation of the line passing through the points (-3, -5) and (6, 1), we can use the point-slope form of the equation, which is given by:
y - y1 = m(x - x1)
where (x1, y1) are the coordinates of one of the points on the line, and m is the slope of the line.
First, let's find the slope (m):
m = (y2 - y1) / (x2 - x1)
where (x2, y2) are the coordinates of the other point on the line.
Using the given points (-3, -5) and (6, 1):
m = (1 - (-5)) / (6 - (-3))
m = 6 / 9
m = 2/3
Now that we have the slope, let's choose one of the points, say (-3, -5), and substitute its coordinates into the point-slope form:
y - (-5) = (2/3)(x - (-3))
Simplify:
y + 5 = (2/3)(x + 3)
To convert this equation into the form Ax + By = C, where A, B, and C are integers with the greatest common divisor 1, we need to eliminate the fraction. Multiply both sides of the equation by 3 to get rid of the denominator:
3(y + 5) = 2(x + 3)
Now, distribute on the left side:
3y + 15 = 2x + 6
Move the terms with y to the left side and the constant term to the right side:
3y - 2x = 6 - 15
Simplify the right side:
3y - 2x = -9
Now, we have the equation of the line in the desired form, with A = -2, B = 3, and C = -9. To ensure that A is positive, we can multiply the entire equation by -1:
-(-2x + 3y) = -(-9)
Simplifying:
2x - 3y = 9
So, the equation of the line in the form Ax + By = C, where A, B, and C are integers with the greatest common divisor 1, and A is positive, is:
2x - 3y = 9