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What does it mean when the question ask are X and Y related linearly.

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5 Answers

 It means that they are related by equation of 
   Y = mx +b
    m is slope, geometrically. It means that rate of change is fixed
    A plumber charges $30 for service and $20 for every hour of work.
  then Cost of fixing depends on number of hours of work done:, and the relation is given by the following equation:
              C = 20t + 30
                 $30 is service charge that is called start of the process
                  $20 is the rate(per unit) change, means that for every hour of work he charges $20 fix.
             Linear relation is where Relation is represented by a binomial Expression( consist of 2 terms)
             the coefficient of the variable( 20) is the fixed rate of change,
               30 is the value of C at start of the point in the context of this problem will be service call.
           In graph of the equation. $30 will be the C(vertical intercept), and $20 will be slope.
           The feature of linear relation is that rate of change, rise/ run and slope is fixed.

if you have a bunch of points represented as (x,y) and if you are able to plot the points on a graph and connect all the lines using a straight line using a scale, you can say the relationship is linear.

for ex:

speed of travel  (x-axis)             Time (x-axis)

       5 mph                                    100 min

       10 mph                                   80 min

       15 mph                                   60 min

       20 mph                                   40 min


Plot these in a graph and let me know, Nice to know you are from Cincy, Go REDS!


If you are looking at a graph of y with relation to x (so y is on the vertical axis and x is on the horizontal), does it look like a line?  If so, then you are dealing with a linear relationship.
If you are looking at a list of points, or a table of corresponding x and y values, look at the difference between x values and the difference between y values.  If every time x goes up, y changes by a constant value, it's a linear relationship.
For instance:
x   y
-1  4
1   7
3   10
5   13
appears to be a linear relationship because every time x goes up by 2, y goes up by 3.  However
x   y
-1  4
1   7
3  4
5   1
is not a linear relationship.  The listed x values still go up by 2, but the y values go up and down.  If you were to plot those points and connect the dots, they would not lie on the same straight line.

I can't see the exact problem you're looking at, but I hope that helps.

If x and y are related linearly, then the change of y over the change of x must be a constant, which is often called as slope.

That's mean that relation between x and y can be represented by Ax+By=C, where A, B and C are integers, and A is non-negative, and, A, B, and C have no common factors other than 1. If we solve this equation for y , we will get slope and y-intercept equation (y=mx+b)