Question

Find the equation of the line that passes through the points (2,3) and (-5,6).

Answer 1

To find the equation of the line that passes through the points (2,3) and (-5,6), we can use the point-slope form of a linear equation, which is given by:

y - y1 = m(x - x1)

where (x1, y1) is one of the given points 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:

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

= (6 - 3) / (-5 - 2)

= 3 / (-7)

= -3/7

Now we can choose either of the given points and substitute it for (x1, y1) in the point-slope form. Let's use (2,3):

y - 3 = (-3/7)(x - 2)

Simplifying the right-hand side, we get:

y - 3 = (-3/7)x + (6/7)

Adding 3 to both sides, we get:

y = (-3/7)x + (27/7)

Therefore, the equation of the line that passes through the points (2,3) and (-5,6) is y = (-3/7)x + (27/7).

Explanation:

Answer 2

First, Fina the slope, m = y2 - y1 / x2-x1
y = 6 - 3 / -5 - 2
y = -3 / 7

Now, y - y1 = m(x - x1)
y - 3 = -3/7(x - 2)
y - 3 = -3/7x + 6/7
y = -3/7x + 27/7

Hope this helps!