Question

Describe 3 ways to determine the slope of a line and the similarities and differences between the methods.

Answer 1

Consider a and b are two point on line... Slope of line: Xa-Xb/Ya-Yb
Another way.. Consider line of equation: 2y+3x+5=0
Slope= -u/v
U=3 (number before x)
V=2 (number before y)

Answer 2

For a linear equation (y = ax + b):
Method 1: Inspection
Simply inspect the coefficient of x, this will be the gradient of the slope.

Method 2: Differentiation
This works in much the same way, as you differentiate to find ƒ'(x) you essentially remove the constant term and the power of x for a linear graph. This value will be a constant.

Method 3: (y - y1)/(y2 - y1)  = (x - x1)/(x2 - x1)
This method is similar to the first method, but has a starting point with different information.
This method only works if you have two points on the line. Simply substitute the values for x1, x2, y1 and y2 into the equation and rearrange until you reach the form y = mx + c, then inspect the value of the coefficient of x, this is the gradient of the line.