What you are going to do is to draw two lines and to find the point where they intersect if there is one. The intersection point, assuming that there is one, is the solution of the two equations; that is, the x-coordinate and the y-coordinate make both equations true.
To plot a line, we need two points. However, there's always room for error, so I like to find at least three points. Then, if one is not on the line, I know I made a mistake and need to look at all three points. We need to find three points that are on each of the two lines. We will connect the three points on each line and put arrows at the ends. The intersection point, as best as we can read it off the graph, is our solution.
Parallel lines never intersect and, thus, the equations describing them have no mutual solution.
LINE 1: y = x + 8
You pick three x values that you are prepared to plot and then find the corresponding y values for those x values. I like to pick x-values that make the calculations easy while getting a little variety.
x = 0 y = x + 8 ==> y = 0 + 8 ==> y = 8 POINT 1: (0,8)
x = –2 y = x + 8 ==> y = –2 + 8 ==> y = 6 POINT 2: (–2,6)
x = 3 y = x + 8 ==> y = 3 + 8 ==> y = 11 POINT 3: (3,11)
Plot these three points, connect them and extend the line segment, then put arrows on the ends of the line segment so that we have a line represented.
Do the same thing for the equation of LINE 2. You don't need to use the same values of x. You can use whatever you wish. However, I would not use huge numbers that would be off your paper.
Let me know how it goes!!
LINE 2: y = −2x − 1
