A line passes through point (3,7) and has a slope of 3/4

So first off how do we even know what a line is? Is there a equation? Yes! The the variables mean or represent anything! Absouletly! In which case we would look at a linear equation! The equation for that is y=mx+b. What do each variable represent? Let me tell you!

y= outcome

m= slope

b= y-intercept

Does the infomation we are given applies to these variables? Yes they do!!

We have the coordinate points (3, 7) and the slope or m which is 3/4. We know that 3/4 is the slope so in the linear equation it would look like this:

y= 3/4x+b

Yet where do the coordinate points go? Or what do they consist of or represent? The represent a point on graph or line. It consist of the x and y values which makes it a coordinate point. A coordinate point is (x, y). In this case x= 3 and y=7.

Now let us put that into the equation!

7= 3/4 (3) +b

7= 2.25 +b (hey you! yes you! 2.25 in a fraction form can actually be 9/4 or 2 and 1/4, but anyways back to the problem)

So we now have 7= 2.25 +b. Yet here's the problem what is b? Our main goal is to know what line passes through (3,7) with a 3/4 slope. Well how about we get b alone.

7 = 2.25 +b

-2.25 2.25

4.75 = b ( hi there again 4.75 can be equivalent to 19/4 or 16 and 3/4, anyways back to the problem again :D)

So now we know what b, let us now put together with the infomation we found and given.

Linear equation => y=mx+b

y= 3/4x + 4.75 <= this is the line that passes through the point (3, 7) with a 3/4 slope.

I really do hope I helped you in anyway. Sorry for taking so long to answer your question. But speaking of question, if you have any, don't be afraid to message me or even comment to my answer. I'm always happy to help. Besides that again, I really do hope you understand this! Have a great day.

p.s. I included a graph from the website Desmos (a great website for graphing I LOVE IT!!!) that can prove this line passes through. It is attached to my answer. Good luck.