Question

How do you find the “m” and “b” of any linear equation?

Answer 1

Hint: In any linear equation, m is the slope and b is the y-intercept and this equation is known as the slope-intercept equation. Here will find the y intercept value for the standard equation and will also take one example to understand it in the better ways.

Complete step-by-step answer:
Any linear equation has the standard form of
 $ y = mx + b $
Where “m” is the slope of the equation
And “b” is the y=intercept
The slope of the line, “m” can be expressed as
 $ m = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}} $
Where $ ({x_1},{y_1}) $ and $ ({x_2},{y_2}) $ are the coordinates of any two points in the given line.
When we place $ x = 0 $ in the standard form of equation $ y = mx + b $
 $ \Rightarrow y = m(0) + b $
Zero multiplied by anything is zero.
 $ \Rightarrow y = 0 + b $
Simplify the above equation-
 $ \Rightarrow y = b $
Therefore, y is the intercept.
Now, let us take one example to make it clearer.
 $ y = 3x + 5 $
Place $ x = 0 $ in the above equation
 $ \Rightarrow y = 3(0) + 5 $
Zero multiplied by anything is zero.
 $ \Rightarrow y = 0 + 5 $
Simplify the above equation-
 $ \Rightarrow y = 5 $
Therefore, y is the intercept.

Note: Always remember the standard form of the linear equation, slope and intercept equation as the y intercept depends on the standard equation. Also, know the basic identities to simplify the equation such as zero when multiplied with any number always gives the resultant value as zero.
The property of the slopes of the two perpendicular lines is always equal to $ ( - 1) $ whereas slopes of two parallel lines are always equal to each other. Parallel lines can be defined as the two lines which are in the same plane and are at equal distance from each other and they never intersect each other whereas the lines which intersect each other at ninety degree are known as the perpendicular lines.