How do you find the equation, x-intercept, and the y-intercept for the line with an y-intercept of 5 and a slope of -1/3?

1 Answer
smendyka
Apr 13, 2017

See the entire solution process below:

Explanation:

We can use the slope intercept formula to write the equation of 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 information from the problem gives:

#y = color(red)(-1/3)x + color(blue)(5)#

The y-intercept was given as part of the problem: #color(blue)(b = 5)# or #(0, 5)#

To find the x-intercept we set #y# equal to #0# and solve for #x#:

#y = color(red)(-1/3)x + color(blue)(5)# becomes:

#0 = color(red)(-1/3)x + color(blue)(5)#

#0 - 5 = color(red)(-1/3)x + color(blue)(5) - 5#

#-5 = color(red)(-1/3)x + 0#

#-5 = color(red)(-1/3)x#

#-3 xx -5 = -3 xx color(red)(-1/3)x#

#15 = color(red)(cancel(color(blakc)(-3))) xx cancel(color(red)(-1/3))x#

#15 = x#

The x-intercept is #15# or #(15, 0)#

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