Question

How do you write \[y=5x+3\] in standard form?

Answer 1

Hint: The degree of an equation is the highest power to which the independent variable (x in this case) is raised. The degree of the equation decides whether the equation is linear or quadratic or cubic, etc. The standard form of the straight line is \[ax+by+c=0\] here \[a\],\[b\], \[c\in \] Real numbers.

Complete step by step answer:
The given equation is \[y=5x+3\], here the highest power to which x is raised is 1. Hence, the degree of the equation is 1. As the degree of the equation is 1, we can say that it is a linear equation or a straight-line equation. We are asked to write this in its standard form. We know that the standard form of a straight-line equation is \[ax+by+c=0\] here \[a\],\[b\], \[c\in \] Real numbers. So, we have to convert the given equation in a similar form.
The given equation is \[y=5x+3\], as we can see that in standard form the terms having x are on the left-hand side of the equation. So, re-writing the equation with the sides flipped, we get \[5x+3=y\].
Subtracting y from both sides of the above equation we get,
\[\Rightarrow 5x+3-y=y-y\]
\[\Rightarrow 5x+3-y=0\]
\[\Rightarrow 5x-y+3=0\]
Now, that the terms in the equation are re-arranged. It is similar to the standard form of the straight-line equation \[ax+by+c=0\].

The standard form of the given equation is \[5x-y+3=0\].

Note: We can also find the values of a, b, and c for this equation by comparing it with standard form. By comparing, we get \[a=5,b=-1\] and \[c=3\] for this equation.
You can also say that this equation has a standard form \[-5x+y-3=0\], this is also correct. As the value of slope, intercepts are not changing by this.