Question

Write an equation of a line with slope \[3\] and \[y-\text{intersect}\] \[6?\]

Answer 1

Hint: Where we have to write an equation of a given line in the slope intercept form. The equation of line can be written as \[y=mx+b.\]
Whereas \[m\] be the slope \[b\] is the \[y-\text{intercept}.\]
Here the coefficient given in the question will be the values written in the form. Also it may be considered as a parameter of the equation. But they do not contain any of the variables.

Complete step by step solution:
Here given, the equation of line with the slope is \[3\] and \[y-\text{intercept}\] is \[6.\]
Now, we have to write the given values in the form of
\[\Rightarrow y=mx+c\]
Where, as \[m\] is the slope and \[b\] is the \[y-\text{intercept}.\]
Now plug the given values in the given form.
\[m=3\] and \[b=6\]
\[\therefore y=3x+6\]
Thus, the required question will be \[y=3x+6.\]

Additional information:
The another way is to write slope intercept form is the standard form of equation and the standard form of equation is written as \[Ax+By+C.\] As you can also change the slope intercept form is in the standard form for better understanding we take the example as, \[y=\dfrac{-3x}{2}+3.\] now isolate the \[y-\text{intercept}\] and add \[\dfrac{3x}{2}\] then the equation we get, \[\dfrac{3x}{2}+y=3.\] But as we have standard form fraction part does not consider their so, we have to solve it, the equation we get \[2\left( \dfrac{3x}{2}+y \right)=3\left( 2 \right)\]
\[\therefore 3x+2y=6.\] Then the given equation is considered as in a standard form equation.

Note: The standard form of a linear equation is one as follows: \[\text{A}x+\text{B}y=\text{C}.\] There are some restriction which you need to remember that is A and B cannot be zero and A and B both are integers and A is positive number. In the standard form no fraction nor decimal accepts in the equation. For example we take \[\dfrac{1}{3}x+\dfrac{1}{4}y=4.\] We can say that the equation is not in the standard from and another examples as \[4x+3y=8\] then the given equation is in the standard form.