Answer :
To determine which points lie on the graph of the equation [tex]\( -3x + 6y + 5 = 7 \)[/tex], we will go through each given point and substitute their coordinates into the equation. We need to see if the equation holds true for the point to be on the graph.
The given equation is:
[tex]\[ -3x + 6y + 5 = 7 \][/tex]
To see if a point [tex]\( (x, y) \)[/tex] lies on this graph, we need:
[tex]\[ -3x + 6y + 5 = 7 \][/tex]
We will substitute the coordinates of each point into this equation and check if it is satisfied.
Point A: [tex]\((-3, 6)\)[/tex]
Substitute [tex]\( x = -3 \)[/tex] and [tex]\( y = 6 \)[/tex]:
[tex]\[ -3(-3) + 6(6) + 5 = 9 + 36 + 5 = 50 \][/tex]
[tex]\[ 50 \neq 7 \][/tex]
Thus, [tex]\((-3, 6)\)[/tex] does not satisfy the equation.
Point B: [tex]\((-2, 0)\)[/tex]
Substitute [tex]\( x = -2 \)[/tex] and [tex]\( y = 0 \)[/tex]:
[tex]\[ -3(-2) + 6(0) + 5 = 6 + 0 + 5 = 11 \][/tex]
[tex]\[ 11 \neq 7 \][/tex]
Thus, [tex]\((-2, 0)\)[/tex] does not satisfy the equation.
Point C: [tex]\((0, -2)\)[/tex]
Substitute [tex]\( x = 0 \)[/tex] and [tex]\( y = -2 \)[/tex]:
[tex]\[ -3(0) + 6(-2) + 5 = 0 - 12 + 5 = -7 \][/tex]
[tex]\[ -7 \neq 7 \][/tex]
Thus, [tex]\((0, -2)\)[/tex] does not satisfy the equation.
Point D: [tex]\((6, -3)\)[/tex]
Substitute [tex]\( x = 6 \)[/tex] and [tex]\( y = -3 \)[/tex]:
[tex]\[ -3(6) + 6(-3) + 5 = -18 - 18 + 5 = -31 \][/tex]
[tex]\[ -31 \neq 7 \][/tex]
Thus, [tex]\((6, -3)\)[/tex] does not satisfy the equation.
Point E: [tex]\((8, 2)\)[/tex]
Substitute [tex]\( x = 8 \)[/tex] and [tex]\( y = 2 \)[/tex]:
[tex]\[ -3(8) + 6(2) + 5 = -24 + 12 + 5 = -7 \][/tex]
[tex]\[ -7 \neq 7 \][/tex]
Thus, [tex]\((8, 2)\)[/tex] does not satisfy the equation.
Since none of the points satisfy the equation [tex]\(-3x + 6y + 5 = 7\)[/tex], none of the points [tex]\( A, B, C, D, \)[/tex] or [tex]\( E \)[/tex] lie on the graph of the equation.
Therefore, there are no points from the given options that are on the graph of the equation [tex]\( -3x + 6y + 5 = 7 \)[/tex].
The given equation is:
[tex]\[ -3x + 6y + 5 = 7 \][/tex]
To see if a point [tex]\( (x, y) \)[/tex] lies on this graph, we need:
[tex]\[ -3x + 6y + 5 = 7 \][/tex]
We will substitute the coordinates of each point into this equation and check if it is satisfied.
Point A: [tex]\((-3, 6)\)[/tex]
Substitute [tex]\( x = -3 \)[/tex] and [tex]\( y = 6 \)[/tex]:
[tex]\[ -3(-3) + 6(6) + 5 = 9 + 36 + 5 = 50 \][/tex]
[tex]\[ 50 \neq 7 \][/tex]
Thus, [tex]\((-3, 6)\)[/tex] does not satisfy the equation.
Point B: [tex]\((-2, 0)\)[/tex]
Substitute [tex]\( x = -2 \)[/tex] and [tex]\( y = 0 \)[/tex]:
[tex]\[ -3(-2) + 6(0) + 5 = 6 + 0 + 5 = 11 \][/tex]
[tex]\[ 11 \neq 7 \][/tex]
Thus, [tex]\((-2, 0)\)[/tex] does not satisfy the equation.
Point C: [tex]\((0, -2)\)[/tex]
Substitute [tex]\( x = 0 \)[/tex] and [tex]\( y = -2 \)[/tex]:
[tex]\[ -3(0) + 6(-2) + 5 = 0 - 12 + 5 = -7 \][/tex]
[tex]\[ -7 \neq 7 \][/tex]
Thus, [tex]\((0, -2)\)[/tex] does not satisfy the equation.
Point D: [tex]\((6, -3)\)[/tex]
Substitute [tex]\( x = 6 \)[/tex] and [tex]\( y = -3 \)[/tex]:
[tex]\[ -3(6) + 6(-3) + 5 = -18 - 18 + 5 = -31 \][/tex]
[tex]\[ -31 \neq 7 \][/tex]
Thus, [tex]\((6, -3)\)[/tex] does not satisfy the equation.
Point E: [tex]\((8, 2)\)[/tex]
Substitute [tex]\( x = 8 \)[/tex] and [tex]\( y = 2 \)[/tex]:
[tex]\[ -3(8) + 6(2) + 5 = -24 + 12 + 5 = -7 \][/tex]
[tex]\[ -7 \neq 7 \][/tex]
Thus, [tex]\((8, 2)\)[/tex] does not satisfy the equation.
Since none of the points satisfy the equation [tex]\(-3x + 6y + 5 = 7\)[/tex], none of the points [tex]\( A, B, C, D, \)[/tex] or [tex]\( E \)[/tex] lie on the graph of the equation.
Therefore, there are no points from the given options that are on the graph of the equation [tex]\( -3x + 6y + 5 = 7 \)[/tex].