An intercept is a point of intersection (a point where a line crosses another line)- Typically, in terms of linear graphs, finding #x# and #y# intercepts are asked, or the intercepts of line with another line.
Let's look at #x# and #y# intercepts. We can consider the #x#-axis as a line, and the #y#-axis as a line. A line can only intersect another line in one point, so there will be one #x#-intercept, and one #y#-intercept for a linear graph. Note that an intercept is a point in the form of (#x,y#)
-To find an #x# intercept, we have to find the point where the line intersects the #x#-axis. To do this, we set #y#=0 and solve the equation for #x#. This makes sense because when y=0, we can only move in the #x#-direction...hence finding the exact value of #x# when #y# is zero.
-To find a #y# intercept, we have to find the point where the line intersects the #y#-axis. To do this, this time we set x=0 and solve the equation for the remaining #y#. This makes sense because when x=0, we can only move in the y-direction, and then find the point where the line crosses that y-axis.
After that we end up with an #x#-intercept in the form of (#x,0#) and a #y#-intercept in the form of (#0,y#).
To find where a line intersects another line, you can solve both equations for #y# (or #x#) and then set them equal to each other. When you set them equal to each other, you end up with one unknown, which you can solve for with some algebra. When you get that unknown, you can plug it into one of the original equations to the other unknown.
Alternatively, we could always graph the line(s) and observe the points of intersection.
For example, to see where the line #y=2x+4 # intersects the axes, you can just look at the graph. You'll see that it intersects the #x#-axis in the point (-2,0) and the #y#-axis in the point (0,4).
graph{2x+4 [-10, 10, -5, 5]}
Notice that if you wanted to find this algebraically, you would set the #y=0# and solve for #x# to find #x=-2# as an intercept, and then set #x=0# and find #y=4# as another.
