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Rate of Change Calculator

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Rate of change is nothing but the slope of a line. If the coordinates of the end points ($x^{1}, y^{1}) and (x^{2}, y^{2}$) of line is given, the Rate of Change calculator wil calculate the slope of the line.

Rate of change formula :

Rate of change (slope of line, m) = $\frac{(y_2 - y_1)}{(x_2 - x_1)}$
 

Steps

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Step 1 : Note the given coordinates of end points of the line.

Step 2 : Using the slope of line equation, plug in the values of $x_1$, $x_2$, $y_1$, and $y_2$ into it and get the slope of line.

Problems

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Let's discuss some of the problems based on rate of change .

Solved Examples

Question 1: Find the rate of change for (-1, -3)(2, -5) ?
Solution:
Step 1 : Given points,
$x_1$ = -1, $x_2$ = 2, $y_1$ = -3, and $y_2$ = -5.

Step 2 : Rate of change (slope of line, m) = $\frac{(y_2 - y_1)}{(x_2 - x_1)}$

                                           = $\frac{(-5 - (-3))}{(2 - (-1))}$

                                           = $\frac{-2}{3}$.
                                           
Therefore, the rate of change of line is $\frac{-2}{3}$.     


Question 2:
Find the rate of change for (0, -3)(5, 4) ?

Solution:
Step 1 : Given points,
$x_1$ = 0, $x_2$ = 5, $y_1$ = -3, and $y_2$ = 4.

Step 2 : Rate of change (slope of line, m) = $\frac{(y_2 - y_1)}{(x_2 - x_1)}$

                                           = $\frac{(4 - (-3))}{(5 - 0))}$

                                           = $\frac{7}{5}$.
                                           
Therefore, the rate of change of line is $\frac{7}{5}$.