Which graph represents the solution to the given system?
Y=-4x+4
Y=1/2x-2
The correct graph is:
To determine the graph that represents the solution to the given system, we need to sketch the lines represented by the equations and identify their point of intersection.
Firstly, let's graph the equation Y = -4x + 4:
Plot the y-intercept: the y-intercept is 4, so plot the point (0, 4).
Find additional points by using the slope: the slope is -4, which means that for every increase of 1 in x, y decreases by 4. So, starting from the y-intercept (0, 4), we can go one unit to the right and four units down to get another point, (1, 0).
Connect the points with a straight line.
Next, let's graph the equation Y = (1/2)x - 2:
Plot the y-intercept: the y-intercept is -2, so plot the point (0, -2).
Find additional points by using the slope: the slope is 1/2, which means that for every increase of 1 in x, y increases by 1/2. So, starting from the y-intercept (0, -2), we can go two units to the right and one unit up to get another point, (2, -1).
Connect the points with a straight line.
Finally, we need to determine the point of intersection between the two lines.
By observing the graph, we can see that the two lines intersect at the point (2, -1).
Therefore, the graph representing the solution to the given system is a single point, which is (2,-1).