Problem Solving

In the xy-coordinate system, if (a,b) and (a+3, b+k) are two points on the line defined by the equation x = 3y-7, then k=

(A) 9
(B) 3
(C) 7/3
(D) 1
(E) 1/3

x=3y-7

Re-write the above equation to slope intercept form (y=mx+b) where m is the slope.

(x+7)/3=y

m=1/3

m=y2-y1/x2-x1

1/3=k/3

1=k

Good work. K=1 is correct. Might sound stupid, but how do you get m = 1/3 from y = (x+7)/3?

Good work. K=1 is correct. Might sound stupid, but how do you get m = 1/3 from y = (x+7)/3?

y=(x+7)/3 simplifies to y=x/3+7/3 and since y=mx+b, where m is the slope, we simply look for the number before the x in order to find the slope of the line. In this case, that number is 1/3. I hope this helps.

So are we basically assuming x/3 is equivalent to 1/3 here? After finding 1/3, how do you find out k is 1. Sorry, I'm still trying to grasp the simple steps in between.

Rewriting the eqn. x=3y-7, you get x-3y=7.

Slope = -(co-efficient of x)/co-efficient of y

Here, slope m = -1/-3=1/3

Hope this helps!!

Still cannot understand why x is 1 or -1? Are we just assuming that b/c it has no coefficient.

EMAN wrote:Still cannot understand why x is 1 or -1? Are we just assuming that b/c it has no coefficient.

@Eman :

As you already know that a line equation is in the form of ax+by+c=0
here: a is the co-efficient of x
b is the co-efficient of y
So if you look at the line equation given to us
x-3y -7=0
this can be rewritten as 1*x + (-3)*y -7=0
And Slope is = -(co-efficient of x)/co-efficient of y
= -(1)/(-3)= 1/3

Hope it clarifies your doubt.