How do you write the point slope form of the equation given (3,-2) and (-4,-1)?

Question

Nathan Axel · Accepted Answer

#(y + color(red)(2)) = color(blue)(-1/7)(x - color(red)(3))#

Or

#(y + color(red)(1)) = color(blue)(-1/7)(x + color(red)(4))# The point slope formula requires the slope and one of the two points we have been given in the problem. First, we need to find the slope which requires two points which we are given in the problem. The slope can be found by using the formula: #m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))# Where #m# is the slope and (#color(blue)(x_1, y_1)#) and (#color(red)(x_2, y_2)#) are the two points on the line. Substituting the values from the problem gives: #m = (color(red)(-1) - color(blue)(-2))/(color(red)(-4) - color(blue)(3))# #m = (color(red)(-1) + color(blue)(2))/(color(red)(-4) - color(blue)(3))# #m = 1/-7# #m = -1/7# Now we can use the point slope formula to create an equation for the line. The point-slope formula states: #(y - color(red)(y_1)) = color(blue)(m)(x - color(red)(x_1))# Where #color(blue)(m)# is the slope and #color(red)(((x_1, y_1)))# is a point the line passes through. Solution 1) Substituting the values from the first point and the slope gives: #(y - color(red)(-2)) = color(blue)(-1/7)(x - color(red)(3))# #(y + color(red)(2)) = color(blue)(-1/7)(x - color(red)(3))# Solution 2) Substituting the values from the second point and the slope gives: #(y - color(red)(-1)) = color(blue)(-1/7)(x - color(red)(-4))# #(y + color(red)(1)) = color(blue)(-1/7)(x + color(red)(4))#

Ethan Adkins · Answer

undefined To write the point-slope form of the equation, use the formula:
$y - y_1 = m(x - x_1)$
where $(x_1, y_1)$ is a point on the line and $m$ is the slope.
Given the points $(3, -2)$ and $(-4, -1)$, first find the slope:
$m = \frac{y_2 - y_1}{x_2 - x_1}$
$m = \frac{-1 - (-2)}{-4 - 3} = \frac{1}{7}$
Choose one of the points, let's say $(3, -2)$, and substitute into the point-slope form:
$y - (-2) = \frac{1}{7}(x - 3)$
Simplify:
$y + 2 = \frac{1}{7}(x - 3)$
This is the point-slope form of the equation.