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A line passes through the points (-3,-5) and (6,1). Write the equation of this line in the form Ax + By = C, where A, B, and C are integers with greatest common divisor 1, and A is positive.

2 Answers

3 votes

Answer:

2x - 3y = 9.

Explanation:

The slope of the line

= (1 - -5) / (6 - -3)

= 6/9

= 2/3.

Using the point-slope form of a straight line:

y - y1 = m(x - x1) where m = the slope and (x1, y1) is a point on the line.

So, using slope m = 2/3 the point (6, 1):

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

y - 1 = 2/3 x - 4

Multiplying through by 3:

3y - 3 = 2x - 12

3y = 2x - 9

2x - 3y = 9.

User MirkoBanchi
by
8.5k points
4 votes

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

User Andrew Alcock
by
8.6k points

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