You can put this solution on YOUR website! First we need to put each equation in slope intercept form
Slope intercept form is:
y = mx + b
m is the slope and
b is y intercept
Ok so the first equation is:
x - 2y = 8
first go ahead a place a 1 in front of the x
this is just a good way to remember that it is there (x=1*x=1x)
1x - 2y = 8
now move the 1x over by subtracting it from both sides
1x - 1x - 2y = -1x + 8
the 1x's on the right side cancel out leaving
-2y = -1x + 8
now divide both sides by -2
-2y/-2 = -1x/-2 + 8/-2
now we have the equation in slope intercept form y = mx + b
and we can easily see that
slope is
and the y intercept is -4
Now we are ready to graph this line
Start at the y intercept
The y intercept is where the line crosses the y axis so this is a known point on the line we are trying to graph.
Since we know that the y intercept for this line is -4
move your pencil to point (0,-4) and mark a dot on the graph
Now lets look at the slope
slope is defined as
The slope for this line is
so we are going to rise up 1 and run to the right 2
Place your pencil over the dot we just marked at point (0,-4)
and rise up 1
you should be at point (0,-3) on the graph
now run to the right 2
you should be at point (2,-3) on the graph
mark a dot here.
Now using a ruler line up the dots and draw a line through them.
Here is what your graph should look like.
Now lets graph the second equation
3x - 2y = 12
Follow the same steps as we did for the first equation
first put the equation in slope intercept form
3x - 2y = 12
3x - 3x - 2y = -3x + 12
-2y = -3x + 12
-2y/-2 = -3x/-2 + 12/-2
Ok so the slope for this line is
and the y intercept is -6
Lets graph it.
Again use the same steps as we did for the first line
start at the y intercept for this line
mark a dot at point (0,-6)
and the slope for this line is
so from point (0,-6)
rise up 3
and run to the right 2
you should be at point (2,-3) on the graph
using a ruler draw a line through both points
now your graph should look like this.
The point at which the lines intersect is the solution for this system of equations.
the point of intersection is (2,-3) This means that for this system of equations x = 2 and y = -3
Lets check these solutions in the original equations
first equation:
x - 2y = 8
substitute x with 2 and y with -3
2 - 2(-3) = 8
2 + 6 = 8
8 = 8
Ok now try the second equation
3x - 2y = 12
3(2) - 2(-3) = 12
6 + 6 = 12
12 = 12
Our solution satisfies both equations so we can be sure we have found the correct solution for this system of equations.
