SOLUTION: My Teacher has been of for ages and came in the other day to give us a homework sheet but the thing is we havent learnt any of this stuff so have looked everywhere on the internet

Question 282417: My Teacher has been of for ages and came in the other day to give us a homework sheet but the thing is we havent learnt any of this stuff so have looked everywhere on the internet for examples but cant find any so thought i would try this site.
The question is:
Find the equation of this line with the y-intercept=2 and passing through (2;6)
Would love if you could help with this question as i find it easier to work out the following questions if i can see how one was done first :) Thanks Youu
Found 3 solutions by nerdybill, richwmiller, solver91311:
Answer by nerdybill(7384)   (Show Source): You can put this solution on YOUR website!
Find the equation of this line with the y-intercept=2 and passing through (2;6)
.
Start with the "slope-intercept" form of the line:
y = mx + b
where
(x,y) specifies a single point on the line
m is the slope
b is the y-intercept
.
Your problem gives a single point at (2,6) and the y-intercept as 2. Plug the given info into the slope-intercept form and solve for m:
y = mx + b
6 = m(2) + 2
6 = 2m + 2
4 = 2m
2 = m
.
Since
m = 2
b = 2
Therefore, the equation of the line is:
y = 2x + 2

Answer by richwmiller(17219)   (Show Source): You can put this solution on YOUR website!
You seem to know that we are dealing with linear equations.
Have you heard of y=mx+b?
m is the slope and b is the y intercept?
Have you heard of this to find slope?
(y-y)/(x-x)=m
So we know two points.
(2,6) and (0,2)
Where did I get (0,2)? the y intercept 2 is when x=0. That means (0,2)
(y-y)/(x-x)=m
6-2/2-0=4/2=2 slope is 2
plug in the new info slope =2 and old info y intercept=2
y=mx+b
y=2x+2
done
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!

If the graph has a -intercept of 2, then the line passes through the point (0, 2). Since you also know that the line passes through (2, 6), you have two points which uniquely determine a line. Use the two point form of the equation of a line:

where and are the coordinates of the two given points.

In other words:

You can do the arithmetic and the simplification.

Point of terminology. You said the question is: "Find the equation of this line with the y-intercept=2 and passing through (2,6)" Technically speaking, you can't do what this question asks. There are an infinite number of equation representations for any given line, so you cannot find "the" equation of a line. The only thing you can do is find "an" equation of a line.

And next time just ask the question. You don't need to make all of those phony excuses about why you need the help. The stuff about your teacher being off for a long time and you not learning this stuff -- Big Fat Lie. The stuff about you "looking all over the internet" -- another Big Fat Lie. Please show us the respect we deserve by not demonstrating that you think we are stupid enough to fall for your "dog ate my homework" excuses.

John

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