Alright, let's solve this step by step:
1. Express [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex]:
We start with the equation:
[tex]\[
3x + y - 9 = 0
\][/tex]
To express [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex], we need to isolate [tex]\( y \)[/tex]. We can do this by subtracting [tex]\( 3x \)[/tex] from both sides of the equation:
[tex]\[
y = 9 - 3x
\][/tex]
So, the equation [tex]\( y = 9 - 3x \)[/tex] expresses [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex].
2. Check whether the point [tex]\((3,0)\)[/tex] lies on the equation:
To check if the point [tex]\((3, 0)\)[/tex] lies on the equation [tex]\( y = 9 - 3x \)[/tex]:
- Substitute [tex]\( x = 3 \)[/tex] into the equation:
[tex]\[
y = 9 - 3(3)
\][/tex]
- Simplify the expression:
[tex]\[
y = 9 - 9 = 0
\][/tex]
Since substituting [tex]\( x = 3 \)[/tex] into the equation results in [tex]\( y = 0 \)[/tex], the point [tex]\((3, 0)\)[/tex] does lie on the equation.
3. Check whether the point [tex]\((2,2)\)[/tex] lies on the equation:
To check if the point [tex]\((2, 2)\)[/tex] lies on the equation [tex]\( y = 9 - 3x \)[/tex]:
- Substitute [tex]\( x = 2 \)[/tex] into the equation:
[tex]\[
y = 9 - 3(2)
\][/tex]
- Simplify the expression:
[tex]\[
y = 9 - 6 = 3
\][/tex]
Since substituting [tex]\( x = 2 \)[/tex] into the equation results in [tex]\( y = 3 \)[/tex], the point [tex]\((2, 2)\)[/tex] does not lie on the equation because we get [tex]\( y = 3 \)[/tex] instead of [tex]\( y = 2 \)[/tex].
In summary:
- The point [tex]\((3, 0)\)[/tex] lies on the equation [tex]\( 3x + y - 9 = 0 \)[/tex].
- The point [tex]\((2, 2)\)[/tex] does not lie on the equation [tex]\( 3x + y - 9 = 0 \)[/tex].
