What is the equation of the line passing through #(8,4)# and #(0,-2)#?

1 Answer
smendyka
Aug 29, 2017

See a solution process below:

Explanation:

First, we need to determine the slope of the line. 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)(-2) - color(blue)(4))/(color(red)(0) - color(blue)(8)) = (-6)/-8 = 3/4#

We know from the point #(0, -2)# the #y#-intercept is #-2#. The #y#-intercept is the point where #x = 0# and the line crosses the #y#-axis.

We can use the slope-intercept formula to write and equation for the line. The slope-intercept form of a linear equation is: #y = color(red)(m)x + color(blue)(b)#

Where #color(red)(m)# is the slope and #color(blue)(b)# is the y-intercept value.

Substituting the slope we calculated and the #y#-intercept value gives:

#y = color(red)(3/4)x + color(blue)((-2))#

#y = color(red)(3/4)x - color(blue)(2)#

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