Answer:
The point (9,5) is on the graph of the equation
The graph of the equation is the set of all points that are solutions to the equation
Step-by-step explanation:
we have the linear equation
[tex]y=\frac{1}{3}x+2[/tex]
This is the equation of the line in point slope form
where
the slope is [tex]m=\frac{1}{3}[/tex]
the y-intercept is [tex]b=2[/tex]
Remember that
If a ordered pair is on the graph of the linear equation, then the ordered pair must satisfy the linear equation
The graph of the equation is the set of all points that are solutions to the equation
Verify each statement
case 1) The graph of the equation is a single point representing one solution to the equation
The statement is false
Because the graph of the equation is the set of all points that are solutions to the equation
case 2) The point (9,5) is on the graph of the equation
The statement is true
Because
For x=9, y=5
substitute the value of x and the value of y in the linear equation
[tex]5=\frac{1}{3}(9)+2[/tex]
[tex]5=3+2[/tex]
[tex]5=5[/tex] ----> is true
so
the ordered pair satisfy the linear equation
therefore
The point is on the graph of the equation
case 3) The graph of the equation is the set of all points that are solutions to the equation
The statement is true
case 4) The point (-3,-1) is on the graph of the equation
The statement is false
Because
For x=-3, y=-1
substitute the value of x and the value of y in the linear equation
[tex]-1=\frac{1}{3}(-3)+2[/tex]
[tex]-1=-1+2[/tex]
[tex]-1=1[/tex] ----> is not true
so
the ordered pair not satisfy the linear equation
therefore
The point is not on the graph of the equation
