Maths-
General
Easy

Question

# The table below shows the distance a train traveled over time. How can you determine the equation that represents this relationships.

Hint:

## 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 + cFirst, 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 + cWe choose the first point (2,25), and using it in the above equation, we have 25 = m.2 + cPutting the value of m in the above relation, we have 25 = 12.5 × 2 + cSimplifying, we have 25 = 25 + cThus, we get c = 25 - 25 = 0So, the y-intercept c = 0Using the value of m and c, we get the required equation, y = 12.5x + 0That is y = 12.5x

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.