$Graph the pair of equations in the same rectangular coordinate system: Y=-2x ; y=-2$

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Y=-2x ; y=-2

Full explanation if possible please.

Algebra

Kaisenkp

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Both equations are special cases of the following equation
\[y=ax+b,\]
which is the equation of a staight line. Indeed
- for $y=-2x$ we have $a=-2$ and $b=0$ in the above equation.
- for $y=-2$ we have $a=0$ and $b=-2$.

To graph a straight line you need to find two points on the graph and joint them together to draw straight line.

The points $(0,0)$ and $(1,-2)$ lies on the graph of $y=-2x$.

The points $(0,-2)$ and $(2,-2)$ lies on the graph of $y=-2$. This is a horizental line with $y=-2$.

See the attached file for the graphs.

1 Attachment

Nirenberg

Nirenberg

Leave a comment if you need any clarifications.
Kaisenkp

Hey sorry, really burnt out on math so I need some clarifications. How did you get the 1 in (1, -2) and the 2 in (2, -2)
Nirenberg

If you let x=1 then from y=-2x you get y=2 (-1)=-2. This is how you get (1,-2).
Nirenberg

The equation y=-2 does not depend on x, so no matter what you choose for x you will always get y=-2. If you let x=2, y will be -2, and hence the point (2,-2) is on the line y=-2.
Nirenberg

In general, to find those points you let x to be a number you like and you compute the y component from the equation.

$Graph the pair of equations in the same rectangular coordinate system: Y=-2x ; y=-2$

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