In this type of equation, as it is written in the form #y=mx+c#. The graph is always a straight line. #y# stands for the #y# coordinate, #m# stands for the gradient, and #c# stands for the #y# intercept.
We can check this by plugging in some values for #x#
#x=-1#
#y=2(-1)-3=-5#
#x=0#
#y=2(0)-3=-3#
#x=1#
#y=2(1)-3#=-1
#x=2#
#y=2(2)-3=1#
#x=3#
#y=2(3)-3=3#
The #y# intercept is always the #y# value when #x=0#, so, therefore, the #y# intercept value #=-3#. As shown in the equation.
As you can see, when the #x# value is increased by one, the #y# value increases by two, or when the #x# value decreases by one, the #y# value decreases by two. Since all the differences are the same, the graph should look like a straight line as pictured below.
Since #m# is #>0#, it is a positive slope, if there was no #m#, there would just be a straight line going across whatever the #y# intercept was, in this case #-3#
When drawing the graph written in the form #y=mx+c#, draw around five points, including some negative, positive, and #0# like I have in the table above.
graph{y=2x-3 [-7.023, 7.024, -3.51, 3.513]}
