We are given equation of line 12x-4y+5=18.
We need to find the Rate of Change for this equation.
Please note: Rate of Change is the another name for Slope of an equation.
So, we need to find the slope of the given linear equation.
In order to find the slope(Rate of change) of the equation, we need to solve equation for y and make it in slope-intercept form y=mx+b.
We need isolate it for y on left side.
We have
12x-4y+5=18.
5 is added on left side of the equation.
We need to get rid 5 from left side first.
The reverse operation of addition is subtraction. So, we need to subtract 5 from both sides.
Subtracting 5 from both sides of the equation, we get
12x-4y+5-5=18-5
12x -4y = 13.
Now, we can see, we have 12x on both sides.
We need to get rid 12x from left side now.
Subtracting 12x from both sides, we get
12x-12x -4y = 13-12x
-4y = 13-12x.
-4 is in front of y, we can remove that -4 by dividing both side (each term) by -4.
We get
-4y/-4 = 13/-4-12x/-4.
On simplifying this step, we get
y = - 13/4 + 3x
Now, let us write this equation in slope-intercept form y=mx+b
y= 3x -13/4.
If we compare y= 3x -13/4 and y=mx+b, we can see that coefficents of x are m and 3.
Therefore, m=3.
m represents slope of the equation.
And slope is the another name of Rate of Change.
Therefore, Rate of Change of the given equation is 3.
