Learn Linear Functions Slope

A linear function is defined as the polynomial function contains the degree of one (y = mx + b). One can learn the linear equation relates a dependent variable with an independent variable in a simple way. The power of the linear function which is not always greater than one where there is no independent variable. A simple linear function with one independent variable (Ax + By + C = 0) traces a straight line when plotted on a graph. It is also called as linear equation. Learning the concept of slope using linear equations is known as learning linear functions slope.

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Learning Linear Functions Forms:

The function is defined by,

f = { ( X, Y)/ Y = mX + b }

where m and b are constants, x and y is called a linear functions. The function derives a straight line while graphing.

Functions such as these gives graph that are straight lines, and, thus, the name linear. Linear functions come in three main forms.

Point Slope Form is given by the equation, m = (y - y1) / ( x – x1)
Slope-Intercept Form is given by the equation, y = mx +b
General Form is given by the equation, Ax + By + C = 0.


Slope of the Linear Functions Learning:

Calculations of rate at which the change takes place can be done under the concept of slope. Slope calculates the rate of change in the dependent variable as the independent variable changes. The slope is denoted by m.

Consider the linear function:

y = mx + b

where, m is the slope of the line and b is the y-intercept. Slope is defined as the ratio of unit change in y to the change in x.

slope m = Change in y / Change in x

=> m = (y_(2) - y_(1))/(x_(2) - x_(1))

Learning Linear Function Slope - Examples:

Find the slope of the line segment relating the following points:
(-1,-2) and (1, 6)

Sol:

Here, x1 = -1        

y1 = -2

x2 = 1        

y2 = 6

slope m = (y2 – y1) / (x2 – x1)

=> m = (6 – (-2) / (1 – (-1))

=> m = (6 + 2) / (1 + 1)

=> m = 8 / 2

=> Slope m = 4


Find the slope of the equation, 9x - 3y = 6

Sol:

9x - 3y = 6

=> -3y = 6 – 9x

=> y = (-1/3)(6 – 9x)

=> y = 3x – 2

It is in the general form, y = mx + b

Therefore, slope m = 3 and y-intercept b = -2.