Answer:
A line passing through the points (0, negative 3) and (2, 0)
Step-by-step explanation:
we have
[tex]y-3=\frac{3}{2}(x-4)[/tex]
This is the equation of a line in point slope form
the slope is m=3/2
the point is (4,3)
Remember that
If a ordered pair lie on the given line, then the ordered pair must be satisfy the equation of the line
Verify each case
1) a line passing through the points (0, negative 3) and (2, 0)
For x=0, y=-3
substitute
[tex]-3-3=\frac{3}{2}(0-4)[/tex]
[tex]-6=-6[/tex] ----> is true
The ordered pair (0,-3) lie on the given line
For x=2,y=0
[tex]0-3=\frac{3}{2}(2-4)[/tex]
[tex]-3=-3[/tex] ----> is true
The ordered pair (2,0) lie on the given line
therefore
This graph represent the given function
2) a line passing through the points (negative 2, 0) and (0, negative 3)
For x=-2, y=0
substitute
[tex]0-3=\frac{3}{2}(-2-4)[/tex]
[tex]-3=-9[/tex] ----> is not true
The ordered pair not lie on the given line
therefore
This graph not represent the given function
3) a line passing through the points (negative 4, negative 3) and (2, 1)
For x=-4, y=-3
substitute
[tex]-3-3=\frac{3}{2}(-4-4)[/tex]
[tex]-6=-12[/tex] ----> is not true
The ordered pair not lie on the given line
therefore
This graph not represent the given function
4) a line passing through the points (negative 1, 1) and (1, 1).
For x=-1, y=1
substitute
[tex]1-3=\frac{3}{2}(-1-4)[/tex]
[tex]-2=-7.5[/tex] ----> is not true
The ordered pair not lie on the given line
therefore
This graph not represent the given function
