graph the following equation
x-y=5
If you can plot points, remember that two points determine a line. So, pick two easy points and plot them. Then draw a line through them.
So, what's easy? How about letting x=0 or y=0? That gives us
0-y=5
y = -5
x-0=5
x=5
So, our two points are
(0,-5) and (5,0)
Now it should be clear. You can always pick other points if you want, but they won't really give you any more information.
If you want x=3, then 3-y=5 and y = -2 so the point (3,-2) is on the line too.
To graph the equation x - y = 5, we will use the slope-intercept form of a linear equation, which is y = mx + b. Here's how to do it:
Step 1: Solve for y
Start with the given equation: x - y = 5
To get y alone on one side of the equation, we need to move the x term to the other side. We can do this by subtracting x from both sides:
-y = -x + 5
Since we want y to be positive, we multiply both sides of the equation by -1:
y = x - 5
Now we have our equation in slope-intercept form.
Step 2: Identify the slope and y-intercept
Comparing the equation to y = mx + b, we can see that the coefficient of x is the slope (m) and the constant term is the y-intercept (b).
In this case, the slope is 1 and the y-intercept is -5.
Step 3: Plot the y-intercept
The y-intercept is the point where the line crosses the y-axis. In this case, the y-intercept is at (0, -5). So mark a point at that location on the graph.
Step 4: Use the slope to find additional points
The slope tells us the change in y for a given change in x. Since the slope is equal to 1, we can use this information to find other points on the line.
Starting from the y-intercept (0, -5), we can move one unit up and one unit to the right since the slope is 1 (rise over run).
Plot another point at (1, -4).
Step 5: Draw a straight line through the points
Connect the two points on the graph with a straight line. The line represents all the points that satisfy the equation x - y = 5.
That's it! You have graphed the equation x - y = 5.