To determine which of the given points lie on the line described by the equation [tex]\( 9y - 8x = 25 \)[/tex], we will check each point one at a time by substituting the coordinates into the equation and verifying whether the equation holds true.
Let's verify each point in turn:
### Point (A) [tex]\((-3,0)\)[/tex]
Substitute [tex]\( x = -3 \)[/tex] and [tex]\( y = 0 \)[/tex] into the equation:
[tex]\[
9(0) - 8(-3) = 25
\][/tex]
Simplify:
[tex]\[
0 + 24 = 25
\][/tex]
[tex]\[
24 \neq 25
\][/tex]
Therefore, point (A) [tex]\((-3,0)\)[/tex] does not lie on the line.
### Point (B) [tex]\((0,-3)\)[/tex]
Substitute [tex]\( x = 0 \)[/tex] and [tex]\( y = -3 \)[/tex] into the equation:
[tex]\[
9(-3) - 8(0) = 25
\][/tex]
Simplify:
[tex]\[
-27 + 0 = -27
\][/tex]
[tex]\[
-27 \neq 25
\][/tex]
Therefore, point (B) [tex]\((0,-3)\)[/tex] does not lie on the line.
### Point (C) [tex]\((-2,1)\)[/tex]
Substitute [tex]\( x = -2 \)[/tex] and [tex]\( y = 1 \)[/tex] into the equation:
[tex]\[
9(1) - 8(-2) = 25
\][/tex]
Simplify:
[tex]\[
9 + 16 = 25
\][/tex]
[tex]\[
25 = 25
\][/tex]
Therefore, point (C) [tex]\((-2,1)\)[/tex] does lie on the line.
### Point (D) [tex]\((1,-2)\)[/tex]
Substitute [tex]\( x = 1 \)[/tex] and [tex]\( y = -2 \)[/tex] into the equation:
[tex]\[
9(-2) - 8(1) = 25
\][/tex]
Simplify:
[tex]\[
-18 - 8 = -26
\][/tex]
[tex]\[
-26 \neq 25
\][/tex]
Therefore, point (D) [tex]\((1,-2)\)[/tex] does not lie on the line.
So, the point that lies on the line [tex]\( 9y - 8x = 25 \)[/tex] is
(C) [tex]\((-2,1)\)[/tex].
