Question

Identify the following equation as that of a line, a circle, an ellipse, a parabola, or a hyperbola.

x + y = 5

Answer 1

This equation is a line

Explanation:

We can tell it's a line because both the x and y values are raised to the first power. In order for it to be any of the others, one or both of the variables would have to have a non-one exponent.

Answer 2

It is a line.

Explanation:

Since, the general equation of,

A line is ax + by = c

A circle is
`(x-h)^2+(y-k)^2=r^2`

An ellipse is
`(x^2)/(a^2)+(y^2)/(b^2)=1`

A parabola is
`y^2=4ax` or
`x^2=4ay`

A hyperbola is
`(x^2)/(a^2)-(y^2)/(b^2)=1`

Where, a, b and c are constants.

Here, the given equation is,

x + y = 5

Which is the type of ax + by = c

Hence, x + y = 5 is a line.