What is the equation of the line that passes through the points (3 , 1) and (-6 , 4)?

Answer 1

To find the equation of the line that passes through two points, we can use the point-slope form of a linear equation:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line, and m is the slope of the line.

First, let's find the slope of the line using the two given points (3, 1) and (-6, 4).

slope = (y2 - y1) / (x2 - x1)

slope = (4 - 1) / (-6 - 3) = 3 / (-9) = -1/3

Now, let's substitute one of the given points into the point-slope form. We can choose (3, 1):

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

Simplifying the equation:

y - 1 = (-1/3)x + 1

Adding 1 to both sides:

y = (-1/3)x + 2

So, the equation of the line that passes through the points (3, 1) and (-6, 4) is y = (-1/3)x + 2.