Question

What do ‘m’ and ‘b’ represent?

Answer 1

Hint: We are given a question with two variables ‘m’ and ‘b’. We are asked to tell what these variables represent. If we see the given variables, we can recollect that these occur in the expression of the slope intercept form, which is expressed as, \[y=mx+b\]. And we know that the terms in the expression have a definite property associated to it. Hence, we will have the answer to what the given variables ‘m’ and ‘b’ represent.

Complete step-by-step answer:
According to the given question, we are given two variables ‘m’ and ‘b’ and we have to tell what these variables refer to or what these variables represent.
If we want to know what these variables mean, we have to recollect what we learnt in equations of lines and the general representation of a line with two variables.
 We know that the equation of a line looks like, \[px+qy=s\]. Now, we have another form of representing the equation of a line, which is, \[y=mx+b\].
This equation, \[y=mx+b\], is called the slope intercept equation.
Here,
‘m’ refers to the slope of the given equation
and ‘b’ refers to the y – intercept of the given equation of a line.
Slope of a line is defined as the change in ‘y’ as the value of ‘x’ changes. This can be represented as \[\dfrac{\Delta y}{\Delta x}\]. If we are given two points like \[\left( {{x}_{1}},{{y}_{1}} \right)\] and \[\left( {{x}_{2}},{{y}_{2}} \right)\], the slope of the line joined by these points can be found by the formula, \[Slope=\dfrac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}\].
The y – intercept refers to the point where the line intersects or cuts the y – axis, so the coordinate at this point can be written as \[\left( 0,b \right)\], that is, x – coordinate is 0 at this point.

Note: The slope intercept form equation of a line should be known else the question will not get solved. Also, the terms used in an equation should be made aware of before using it to find the slope and the y – intercept. So, if we have to find the value of the slope and y – intercept, we have to first modify the given equation to look something like \[y=mx+b\], then we can compare the equations and find the required.