What is the slope-intercept form of the line passing through # (-2, -1)# and # (0, -6) #?

1 Answer
smendyka
May 2, 2017

See the entire solution process below:

Explanation:

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.

First 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)(-6) - color(blue)(-1))/(color(red)(0) - color(blue)(-2)) = (color(red)(-6) + color(blue)(1))/(color(red)(0) + color(blue)(2)) = -5/2#

The point #(0, -6)# is the y-intercept (the value of #y# when #x# is #0#).

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

#y = color(red)(-5/2)x + color(blue)(-6)#

#y = color(red)(-5/2)x - color(blue)(6)#

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