How do you graph the equation #y=4x-2#?

1 Answer
May 20, 2017

The general equation for a line is #y = mx + b#, where:

  • #y# is the dependent variable (dependent on #x#).
  • #m = (y_2 - y_1)/(x_2 - x_1)# is the slope.
  • #x# is the independent variable.
  • #b# is the y-intercept.

Match that up to the general form:

#y = 4x - 2#

#=> m = 4#
#=> b = -2#

This means the slope describes an increase in #y# of #4# for every increase in #x# of #1#:

#m = (y_2 - y_1)/(x_2 - x_1) = 4/1#

This also means that the graph crosses the #y# axis at #y = -2#, the y-intercept where #x = 0#. This means that:

  • #(0,-2)# is a point on the graph.
  • Applying the slope onto #(0,-2)#, we get that #(0+1,-2+4) = (1,2)# is another point on the graph.

Two points make a line, so you have your graph:

graph{4x - 2 [-10, 10, -5, 5]}

And you should spot where #(1,2)# is on the graph to verify that it is there.