Graphing the two equations visually illustrates the point where they intersect, providing a solution to the system of linear equations.
To solve the system of linear equations y = -2x - 8 and y = 2/5x + 4 by graphing, we can plot both equations on the same set of axes and identify the point where they intersect.
Firstly, consider the equation y = -2x - 8. This is a linear equation in slope-intercept form (y = mx + b), where the slope (m) is -2, and the y-intercept (b) is -8. Plotting this line on the graph, we can identify its slope and intercept.
Similarly, the equation y = 2/5x + 4 is also in slope-intercept form. Here, the slope is 2/5, and the y-intercept is 4. Plotting this line will give us another set of points.
The point of intersection of the two lines represents a solution to the system. By visually inspecting the graph, we can determine the coordinates where the lines intersect.
After finding the point of intersection, substitute the x and y values back into either of the original equations to ensure they satisfy both equations.