We know that
if the point belongs to the graph, then it must satisfy the given function.
We proceed to verify each of the points
we have
[tex] f(x) = 7 - 3x [/tex]
case a) [tex] (-2, 1) [/tex]
[tex] x=-2\\y=1 [/tex]
Substitute the value of x in the given function and compare the value of f(x) with the value of the coordinate y of the point
[tex] f(x) = 7 - 3*(-2) [/tex]
[tex] f(x) = 13 [/tex]
[tex] 13\neq 1 [/tex] --------> the point not lie on the graph
case b) [tex] (-1, 10) [/tex]
[tex] x=-1\\y=10 [/tex]
Substitute the value of x in the given function and compare the value of f(x) with the value of the coordinate y of the point
[tex] f(x) = 7 - 3*(-1) [/tex]
[tex] f(x) = 10 [/tex]
[tex] 10=10 [/tex] --------> the point lie on the graph
case c) [tex] (0, 7) [/tex]
[tex] x=0\\y=7 [/tex]
Substitute the value of x in the given function and compare the value of f(x) with the value of the coordinate y of the point
[tex] f(x) = 7 - 3*(0) [/tex]
[tex] f(x) = 7 [/tex]
[tex] 7=7 [/tex] --------> the point lie on the graph
case d) [tex] (1, 5) [/tex]
[tex] x=1\\y=5 [/tex]
Substitute the value of x in the given function and compare the value of f(x) with the value of the coordinate y of the point
[tex] f(x) = 7 - 3*(1) [/tex]
[tex] f(x) = 4 [/tex]
[tex] 4\neq 5 [/tex] --------> the point not lie on the graph
case e) [tex] (2, 1) [/tex]
[tex] x=2\\y=1 [/tex]
Substitute the value of x in the given function and compare the value of f(x) with the value of the coordinate y of the point
[tex] f(x) = 7 - 3*(2) [/tex]
[tex] f(x) = 1 [/tex]
[tex] 1=1 [/tex] --------> the point lie on the graph
therefore
the answer is
Points that lie on the graph are
[tex] (-1, 10) [/tex]
[tex] (0, 7) [/tex]
[tex] (2, 1) [/tex]
see the attached figure to better understand the problem
