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What is the equation in point slope form that passes through the points (2, 1) and (-3, -6)?

Question

What is the equation in point slope form that passes through the points (2, 1) and (-3, -6)?
What is the equation in point slope form that passes through the points (2, 1) and (-3, -6)?

Answers

#y - 1 = 7/5(x - 2)#

or

#y + 6 = 7/5(x + 3)#

Explanation:

Point slope form is written as #y - y_1 = m(x - x_1)#

Use the slope formula with the two given points to find the slope of the line.

#m = (1 - (-6))/(2 - (-3)) = 7/5#

Now that we have our m, we can insert the x and y values of either point to create our line. We'll use (2, 1).

#y - 1 = 7/5(x - 2)#

To check it, we can use the other point, (-3, -6)

#-6 - 1 = 7/5(-3 - 2)#

#-7 = 7/5 * -5#

#-7 = -7#

We can also say #y + 6 = 7/5(x + 3)# and check with (2,1)

#1 + 6 = 7/5(2 + 3)#

#7 = 7#


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