Question
The table below shows the distance a train traveled over time. How can you determine the equation that represents this relationships.
Hint:
We are given the relationship between time and distance travelled by a train. We find the equation representing this relationship in the slope-intercept form which is y = mx + c. First we find the slope (m) of the equation from the given data and then find the y-intercept (b). We then use these two values to get the final equation.
The correct answer is: y=12.5x
Step by step solution:
We denote the time on the x-axis and distance on the y-axis.
Let the equation be denoted by y = mx + c
First, we find the slope of the equation.
For two points 
and 
satisfying the equation, the slope is given by
Taking any two points from the table and denoting them as
, we have
Next, for finding the y-intercept, we input any value from the table in the equation
y = mx + c
We choose the first point (2,25), and using it in the above equation, we have
25 = m.2 + c
Putting the value of m in the above relation, we have
25 = 12.5 × 2 + c
Simplifying, we have
25 = 25 + c
Thus, we get
c = 25 - 25 = 0
So, the y-intercept c = 0
Using the value of m and c, we get the required equation,
y = 12.5x + 0
That is
y = 12.5x
Taking any two points from the table and denoting them as
, we haveNext, for finding the y-intercept, we input any value from the table in the equation
We choose the first point (2,25), and using it in the above equation, we have
Putting the value of m in the above relation, we have
Simplifying, we have
Thus, we get
So, the y-intercept c = 0
Using the value of m and c, we get the required equation,
That is
Instead of using these particular points to find the slope and the y-intercept, we can use any other points from the table; we will get the same equation at the end. We can also verify this equation by inserting the points from the table and checking if the equation is satisfied. Finally, we can find the line in any other forms of a straight line.
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