Determine whether the graphs of the equations are parallel, perpendicular, or neither.
y=-x+2
y=-x-3
they are parallel
To determine whether the graphs of two equations are parallel, perpendicular, or neither, we need to compare their slopes.
Let's start with the given equations:
Equation 1: y = -x + 2
Equation 2: y = -x - 3
Both equations are in slope-intercept form, y = mx + b, where m is the slope.
Comparing the slopes, we can see that both equations have a slope of -1. Since the slopes are the same, we can conclude that the graphs of these equations are parallel.
However, it's always a good idea to graph the equations to visually confirm our result. Let's plot the points:
For Equation 1, when x = 0, y = -0 + 2 = 2. So, we have the point (0, 2).
When x = 1, y = -1 + 2 = 1. So, we have the point (1, 1).
For Equation 2, when x = 0, y = -0 - 3 = -3. So, we have the point (0, -3).
When x = 1, y = -1 - 3 = -4. So, we have the point (1, -4).
Plotting these points on a graph, we can see that both equations have the same slope (-1) and are parallel lines.
Thus, the answer is that the graphs of the equations y = -x + 2 and y = -x - 3 are parallel.