Hopefully you know how to isolate a variable. But if not lets isolate the y-variable together.
-3x + 4y = 8 Add 3x to both sides. *You can also chose to subtract 4y from both sides and still get the same result, but I'll leave that as an exercise for you.
4y = 3x +8 Now divide both sides by 4. *Often students forget to put + 8 because the positive sign isn't there.
4y/4 = 3x/4 + 8/4 Simplify. *Divide the 3 and 8 each by 4 because they are separated by a plus(or minus) sign. Its a different story when there's multiplication or division. If you need help understanding that just let me know.
y = 3x/4 + 2 Final equation. * "Why isolate for y?" I can answer that too but for the mean time just do it.,
You only need two points to plot a graph for a linear equation ( a line). *"There are other types of equations?" you might ask? Yes but don't worry about them right now.
It's always a great choice to pick zero as the first number you use for x.
y = 3(0)/4 + 2
y=2 You just found the y-intercept! It's where the graph of the line crosses the y (vertical) axis.
You could pick any other number for the second x-value but look closer at the final equation. it has a fraction. so how can we use this to our advantage? we have to try and use a number for x that makes the fraction turn into in integer( a non-fraction or a non-decimal). You could use a 4 because it will turn out like this:
y = 3(4)/4 + 2 The 4's will cancel and
y= 3 + 2
y = 5
Now all you have to do is use the two points. (0,2) and (4,5). This is the format for a point (x,y) *Some students have trouble with this, but if you need help just let me know.
So lets plot the points on a graph.
Now draw a line through the points ( a ruler helps) to see the line.
That's it. I hope this helps. Post to this thread if you want me to clarify anything else.
Have a great day!