In order to graph the given equations, let's find their x-intercepts and y-intercepts. Let's start with the first equation.
3x+y=6
In order to find x-intercept, we substitute y with 0 into the equation.
The y-intercept of the graph of our equation is (0,6). Now we are ready to draw the graph of our equation by using interception points. However, let's first find the x- and y-intercepts of the other equations. We will follow the exact same method.
Equations
x=0
y-intercept
y=0
x-intercept
3x+y=6
3( 0)+y=6
(0,6)
3x+ 0=6
(2,0)
3x-y=6
3( 0)-y=6
(0,-6)
3x- 0=6
(2,0)
-3x+y=6
-3( 0)+y=6
(0,6)
-3x+ 0=6
(-2,0)
We are ready to go! Let's draw them on the same coordinate plane. This way we will be able to see the differences and similarities more clearly.
Now, let's interpret the graphs point by point.
3x + y = 6 and -3x + y = 6 have the same y-intercept but different x-intercepts. We can also say that they are symmetric about the y-axis. Therefore, they have different slopes.
3x +y =6 and 3x -y = 6 have the same x-intercept. However, their y-intercepts are different. We can also notice that they are symmetric about the x-axis. Therefore, they have different slopes.
-3x + y = 6 and 3x - y = 6 have different x- and y-intercepts and we can see that they are parallel. Therefore, they have the same slope.
