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?

Question

Kennedy Adams · Accepted Answer

See the entire solution process below:

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)#

Kennedy Adams · Answer

undefined To find the equation of the line, we use the slope-intercept form: $ y = mx + b $, where $ m $ is the slope and $ b $ is the y-intercept.
Given the y-intercept $ b = 5 $ and slope $ m = -\frac{1}{3} $, the equation of the line is $ y = -\frac{1}{3}x + 5 $.

To find the x-intercept, we set $ y = 0 $ in the equation and solve for $ x $:
$$ 0 = -\frac{1}{3}x + 5 $$
$$ \frac{1}{3}x = 5 $$
$$ x = 5 \times 3 = 15 $$

Therefore, the x-intercept is $ (15, 0) $.

To find the y-intercept, we simply use the given y-intercept, which is $ (0, 5) $.