Question

How do you find whether or not a coordinate (don't have a specific example) lies on a particular line? Also, what does Y = MX+ C stand for?

Answer 1

y=mx+b is the equation of a straight line or y=mx+c, must be in the UK yeah? :P

When you use y = mx+b to graph,

the y represents how far up
the x represents how far long
m is the slope (steepness of the line)
b is the y - intercept, where the line crosses the y - axis



This is an example of where m (slope) = 2

\[m = \frac{ y_{2}-y _{1} }{ x _{2}-x _{1} }\]

Basically saying,

\[m = \frac{ Change ~ In ~ Y }{ Change ~ In ~ X }\]

and you can see in the graph, that b = 1 since that's where the line crosses the y - axis.

In y = mx+ b form your solution would be y=2x+1

Another common example, is find the equation of a straight line that has a slope m = 4 and passes though the point (-1, -6).

Once again we look at y = mx+b formula, and we see we need to find b (y - intercept).

-6=4*-1+b
-6=-4+b
-2 = b

Once you find b you can use y = mx+b form again and put it all together

so you get y = 4x- 2

Another way to solve a problem like this would be to use the point - slope form.

\[y-y _{1}=m(x-x _{1})\]

Where the \[(x _{1}, y _{1})\] would represent your coordinate.

so you'd get,

y - (-6) = 4(x-(-1))
y + 6 = 4(x+1)
y+6 = 4x+4
y = 4x+4-6
y = 4x-2

You can see that it's similar when we were using y = mx+b form.

Well I hope that helps you somewhat, take care :)!