y= 2/3x+ 4/3
Step-by-step explanation:
Hi there hopefully I can help you! Okay let us start, what is the equation of a line that is parallel to −2x+3y=−6 and passes through the point (−2, 0)? Well let think, what is the equation or HOW do we find the equation of a line? Well that's simple! We need to look at the linear equation formula? What is that? It is y=mx+b. What do these variables or letters represent?
y= outcome
m= slope (can be (+), (-), a decimal or even a fraction!!)
b= y-intercept (this can also be (+), (-), a decimal or even a fraction!!)
Well how do we still find the equation with the given information? That is tricky, why? Because look at the equation we are given and the linear equation formula?
-2x+3y=-6 y=mx+b (see the differences? yes? no? Hopefully yes)
Why isn't alone and we don't see a y-intercept ( at the moment). So the main question is HOW can we get it into the linear equation formula format? Well simple, ALGEBRA TIME!!!
So first thing we want "y" all alone on one side and "x" on the other
1. Add "2x" to both sides => this will cause the -2x and (+)2x to cancel on one side
-2x+3y=-6
+2x +2x
3y= 2x-6 (Wait, you thought we were done? NOPE)
2. Next, we need to get "y" all alone. How do we do that, we divide the equation by 3.
3y= 2x-6 or => 3y = 2x-6 (some people do this way, your choice.)
3 3 3
(remember a negative number divided by a positive number will result in a negative number)
3. After dividing you should have "y" completely alone on 1 side.
y= 2/3x-2
Hey guess what? We are still not done yet! But we are close to finding the answer, isn't that cool!? Yes it is.
Let keep in mind that this line is parallel to the linear equation yet passes through the coordinate points (-2,0). So first thing is what does parallel mean anyways? Parallel is when two things or lines that intersect (cross) each other at all. So if someone says the lines on the graph are parallel, that means the line doesn't touch and just keep going forever!
But here's the thing, parallel lines can have the same slope, yet different y-intercept!! Don't believe me try using a graphing calculator and put in y=3x+1 and y=3x-2. But anyways! Let us use the information we received and found and find this line that is parallel to our corrected original one.
So we know parallel lines have the same slope. Our "m" or slope we got is 2/3. Okay? Now what? Well we have coordinate points right? Yes we do. What we need to do is input the coordinate points into the equation. We do know a coordinate point is made up of the x and y values so "x" would be -2 and "y" is 0. Let input this into the equation we have
y=mx+b
0= 2/3 (-2) + b
0= -4/3 + b (remember a negative times a positive number will be negative)
0= -4/3 + b (next we need to add 4/3 on both sides to get b alone!)
+4/3 +4/3
4/3 = b (final answer)
So let bring ALL the things we found and put them into an equation!
y=mx+b
y= 2/3x+ 4/3
I really do hope this helps you out a lot! And sorry for typing so much, this is the only way I explain things, very detailed lol. But if you have any questions or comments, don't be afraid to message me! I really do hope you understand and have a great day. :D
P.S. => I do have a little picture of the rules based on dividing by positive and negative. and I also have a graph to help you see that the answer is right! The green line is the y= 2/3x-2 and the black line is the y= 2/3x-2 .
