To solve a system of equations graphically, plot each line on a graph using the slope-intercept form, y = mx + b, by marking the y-intercept and using the slope to find more points. The intersection of the two lines provides the solution.
Step-by-step explanation:
To solve the system of equations graphically, we first understand that both equations given are in the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. The slope represents the steepness of the line and is calculated as the rise over the run, while the y-intercept is the point where the line crosses the y-axis.
For example, if an equation of the line is y = 3x + 9, the slope (m) is 3 and the y-intercept (b) is 9. This means the line crosses the y-axis at the point (0, 9) and for every 1 unit we move to the right (along the x-axis), we move up 3 units (along the y-axis).
To graph these lines, you start by plotting the y-intercept on the y-axis and then using the slope to find another point. For instance, starting at (0, 9), since the slope is 3, you would go up 3 units and to the right 1 unit to reach the next point (1, 12). Plot at least two points for each line based on the slope and y-intercept, then draw a straight line through the points. The point of intersection of the two lines gives the solution to the system of equations.