Final answer:
To graph a system of linear equations and find their intersection point, plot each line using the slope and y-intercept, then look for where the lines cross. This intersection represents the solution to the system of equations. Adjust the y-intercept to shift lines up or down, keeping the slope constant.
Step-by-step explanation:
To graph a system of linear equations and find the intersection point, you should plot each line on a graph with x on the horizontal axis and y on the vertical axis. From Figure A1, we are given that we have a line with a y-intercept of 9 and a slope of 3. This means the line will cross the y-axis at the point (0,9), and for every 1 unit you move to the right (along the x-axis), you will move up 3 units on the y-axis.
To plot this line, start at the y-intercept (0,9). Then, use the slope to find another point: from (0,9), move 1 unit right (to x=1) and 3 units up (to y=12). The second point will be (1,12). Draw a straight line through these two points, and this is the graph of the line.
If you have a second line to graph as part of the system, you would follow the same steps. Once both lines are on the graph, the intersection point is where the two lines cross. This point is the solution to the system, giving you the values of x and y that satisfy both equations simultaneously.
If a line has a larger y-intercept, imagine shifting the entire line up so that it intersects the y-axis at the higher value, keeping the slope unchanged. Alternatively, if it has a smaller y-intercept, shift the line down. This will give you a set of parallel lines each time.
When using algebra to solve systems of equations, such as in economic models, you would typically solve for the variables that satisfy all equations involved. Usually, this involves methods such as substitution, elimination, or using matrices.