solve for x

Question

y= mx + b

Answer 1

What a great opportunity to learn about the equations for lines!
 
The problem gives the equation for a line in slope-intercept form (y = mx + b).  m is the slope (often called "rise over run" because it is the increase in the y value per unit increase in the x variable).
 
Now, solving for x involves subtracting b  from both sides, then dividing the result by m:
         y - b = mx
         (y-b)/m = x
         x = (1/m)y - (b/m)  
This form is important because it tells us that the change in y per unit change in x is (1/m) -- that's the inverse of the slope in the original equation.  And, the x-intercept (the value of x when y=0) is (-b/m).  Now, given the equation of a line in slope-intercept form, it is super-easy to find the x-intercept!
 
So, we can look at an equation like:    y = 2x + 4   and say the y-intercept (the y-value when x=0 and the place where the line crosses the y-axis) is 4.  Also, the x-intercept (the x-value when y=0 and the place where the line crosses the x-axis is  (-b/m) = -4/2 = -2.  Thus, two points on this line (if we need to quickly identify two points) are (0,4) and (-2,0).
 
p.s., there are cases where y is a function of x (a line), but x is not a function of y.  What are they?

 

 

 

THX, Michael!  I can correct my typo, but you can't.  So, you sacrificed for me (that's appreciated).
     See--  http://p1.kciuk.pl/p1.kciuk.pl/5699fb9403d8187caf27fffc0d1d564e.jpg

Answer 2

Solving equations like this, where they want you to find one variable in terms of others, is really the same as solving with all numbers:

 

y = mx + b

 

They want you to solve for x.  So first get the term with x alone by subtracting b from both sides:

 

y - b = mx + b - b

y - b = mx

 

Divide both sides by m:

(y - b) / m = mx / m

(y - b) / m = x

 

So the answer is x = (y - b) / m