How do you write the equation in point slope form given (4,0) and (0,5)?

Question

Ethan Adkins · Accepted Answer

#(y - color(red)(0)) = color(blue)(-5/4)(x - color(red)(4))#

Or

#(y - color(red)(5)) = color(blue)(-5/4)(x - color(red)(0))# First, we must determine the slope. 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 points in the problem gives: #m = (color(red)(5) - color(blue)(0))/(color(red)(0) - color(blue)(4)) = 5/-4 = -5/4# 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. Substituting the slope we calculate and the first point from the problem gives: #(y - color(red)(0)) = color(blue)(-5/4)(x - color(red)(4))# We can also substitute the slope we calculate and the second point from the problem giving: #(y - color(red)(5)) = color(blue)(-5/4)(x - color(red)(0))#

Eli Assouline · Answer

undefined The point-slope form of a line's equation is $y - y_1 = m(x - x_1)$, where $m$ is the slope and $(x_1, y_1)$ is a point on the line.

First, find the slope ($m$) using the two points $(4, 0)$ and $(0, 5)$:

$$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - 0}{0 - 4} = -\frac{5}{4}$$

Using the point-slope formula with one of the points, say $(4, 0)$, we get:

$$y - 0 = -\frac{5}{4}(x - 4)$$

So, the equation in point-slope form is $y = -\frac{5}{4}(x - 4)$.