How do you find the x and y-intercept given #y= 4x - 7#?

1 Answer
Sudip Sinha
Jul 27, 2015

x-intercept = #7/4#
y-intercept = #-7#

Explanation:

There is a very standard way to solve such problems. Let us take an equation of a line in standard form: # y = m x + c #, where #m# is the slope and #c# is the y-intercept.

Firstly, get all the variables to the left-hand side (LHS) and the constant to the right-hand side (RHS). So, we get:
# -m x + y = c #

Now divide the whole equation by the constant on the RHS (note that this does not change the equation), and write it in the form below:
# -m x/c + y/c = 1 # (Dividing by #c#)
# x/(-c/m) + y/c = 1 # (Dividing by #c#)

In this form, the term below #x# (here: #-c/m#) gives the x-intercept and the term below #y# (here: #c#) gives the y-intercept.

Let us turn our attention to the question given. We have:
# y = 4x - 7 #
# => 4x - y = 7 #
# => x / (7/4) + y / (-7) = 1 #
Thus the x-intercept is #7/4# and the y-intercept is #-7#.

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