what is y=6x+3

Question

Cant figure it out. also, what is 12x +3y= -9

Answer 1

Cody,

 

(y = 6x +3) is a linear algebraic equation in one unknown variable, x.  More generally, it is a simple function that maps x into y.  Think of it as a black box that you can't see inside, where either a computer or I sit waiting for you to give me (as input) a value for x, say x=+9, then I compute the y by replacing every x with +9 which turns the algebra into plain arithmetic, and finally I spit out (as output) y = +57 back to you.  So I've mapped x=+9 to y=+57 for you, and can do it again for any other value of x, positive, negative, integer, rational, real, etc.

 

Secondly, it is already in the (y = mx + b) standard slope intercept form, where the slope (m) is +6 and the y-intercept is +3. If x =1, then y =9.  If you were to plot it on an x-y graph, it would be a straight line (because x is only to the first power).  At x=0, y would be +3, the y-intercept. And the slope (m) means for each step of 1 along the x-axis, y moves 6 steps. If x moves positive, so does y move positive because the slope is positive. I x moves negative, so does y move negative.  If m was negative, the x & y would move in opposite directions.

 

Now for your other equation, rearrange its terms to put it into standard slope-intercept form:

12x + 3y = -9  is same as 3y = -12x -9  which reduces to  y = -4x - 3.

 

In this case, it is plotted as a straight line that has slope m=-4 and y-intercept b=-3.