which ordered pairs represent points on the graph of this equation? select all that apply.\n$6y = 7x…

which ordered pairs represent points on the graph of this equation? select all that apply.\n$6y = 7x - 4$\n$(-4, 3)$ $(6, -7)$ $(2, -4)$\n$(4, 4)$ $(-6, 3)$ $(-2, -3)$

which ordered pairs represent points on the graph of this equation? select all that apply.\n$6y = 7x - 4$\n$(-4, 3)$ $(6, -7)$ $(2, -4)$\n$(4, 4)$ $(-6, 3)$ $(-2, -3)$

Answer

To determine which ordered pairs ((x, y)) lie on the graph of the equation (6y = 7x - 4), we substitute the (x) and (y) values of each ordered pair into the equation and check if both sides are equal.

For ((-4, 3)):

Substitute (x = -4), (y = 3):
Left - hand side (LHS): (6y=6\times3 = 18)
Right - hand side (RHS): (7x - 4=7\times(-4)-4=-28 - 4=-32)
Since (18\neq - 32), ((-4, 3)) is not on the graph.

For ((6, -7)):

Substitute (x = 6), (y=-7):
LHS: (6y = 6\times(-7)=-42)
RHS: (7x - 4=7\times6-4 = 42 - 4 = 38)
Since (-42\neq38), ((6, -7)) is not on the graph.

For ((2, -4)):

Substitute (x = 2), (y = -4):
LHS: (6y=6\times(-4)=-24)
RHS: (7x - 4=7\times2-4=14 - 4 = 10)
Since (-24\neq10), ((2, -4)) is not on the graph.

For ((4, 4)):

Substitute (x = 4), (y = 4):
LHS: (6y=6\times4 = 24)
RHS: (7x - 4=7\times4-4=28 - 4 = 24)
Since (24 = 24), ((4, 4)) is on the graph.

For ((-6, 3)):

Substitute (x=-6), (y = 3):
LHS: (6y=6\times3=18)
RHS: (7x - 4=7\times(-6)-4=-42 - 4=-46)
Since (18\neq - 46), ((-6, 3)) is not on the graph.

For ((-2, -3)):

Substitute (x=-2), (y=-3):
LHS: (6y=6\times(-3)=-18)
RHS: (7x - 4=7\times(-2)-4=-14 - 4=-18)
Since (-18=-18), ((-2, -3)) is on the graph.

So the ordered pairs that lie on the graph of (6y = 7x - 4) are (\boldsymbol{(4, 4)}) and (\boldsymbol{(-2, -3)}).