Answer: The first equation is an equation of a parabola. The second equation is an equation of a line.
Explanation:
The first equation is,
[tex]10+y=5x+x^2[/tex]
In this equation the degree of y is 1 and the degree of x is 2. The degree of both variables are not same. Since the coefficients of y and higher degree of x is positive, therefore it is a graph of an upward parabola.
The second equation is,
[tex]5x+y=1[/tex]
In this equation the degree of x is 1 and the degree of y is 1. The degree of both variables are same. Since both variables have same degree which is 1, therefore it is linear equation and it forms a line.
Therefore, the first equation is an equation of a parabola. The second equation is an equation of a line.
Using function concepts, it is found that:
The first equation is:
[tex]10 + y = 5x + x^2[/tex]
Placing in standard format:
[tex]y = x^2 + 5x - 10[/tex]
It is a 2nd degree equation, which is a parabola.
The second equation is:
[tex]5x + y = 1[/tex]
Placing in standard format:
[tex]y = 1 - 5y[/tex]
It is a 1st degree equation, which is a line.
A similar problem is given at https://brainly.com/question/17034119
