Which graph represents the solution to the given system?
Y=-x+2
Y=1/2x+8
The graph representing the solution to the given system would be graph C, the one that intersects both equations at the point (4, 6).
To find the graph that represents the solution to the given system of equations, we can plot both equations on a graph and look for the point(s) of intersection.
The first equation is Y = -x + 2. To graph this line, we can start by plotting the y-intercept, which is 2, then using the slope of -1 (rise of -1 and run of 1) to find one more point to connect and extend the line.
The second equation is Y = (1/2)x + 8. Similarly, we can start by plotting the y-intercept, which is 8, and then use the slope of 1/2 (rise of 1 and run of 2) to find one more point to connect and extend the line.
Plotting both lines on the same graph will give us the solution.
To find the graph that represents the solution to the given system of equations, we need to graph both equations on the same coordinate plane and identify the point(s) where the graphs intersect. The coordinates of the intersection point(s) represent the solution to the system.
Let's graph the first equation, Y = -x + 2:
1. Plot the y-intercept: The y-intercept is the point where the graph intersects the y-axis. In this equation, the y-intercept is 2, so plot the point (0, 2).
2. Plot another point: To find another point on the graph, choose an x-value and substitute it into the equation to find the corresponding y-value. Let's choose x = 1. Substituting this into the equation, we have Y = -(1) + 2, which gives us Y = 1. So plot the point (1, 1).
3. Draw a straight line through the two plotted points. This line represents the graph of Y = -x + 2.
Now let's graph the second equation, Y = (1/2)x + 8:
1. Plot the y-intercept: The y-intercept is at point (0, 8).
2. Plot another point: Choose an x-value and substitute it into the equation to find the corresponding y-value. Let's choose x = 2. Substituting this into the equation, we have Y = (1/2)(2) + 8, which gives us Y = 9. Plot the point (2, 9).
3. Draw a straight line through the two plotted points. This line represents the graph of Y = (1/2)x + 8.
Now, the graph that represents the solution to the system of equations is the intersection point(s) of the two lines we just graphed.