Given:
The given point is (4,12).
To find:
The equation that would NOT contain the point (4,12).
Solution:
We need to check each equation for the point (4,12).
In option A, the given equation is:
[tex]y=-2x+20[/tex]
Putting [tex]x=4[/tex], we get
[tex]y=-2(4)+20[/tex]
[tex]y=-8+20[/tex]
[tex]y=12[/tex]
This equation contains the point (4,12).
In option B, the given equation is:
[tex]y=\dfrac{1}{2}x+8[/tex]
Putting [tex]x=4[/tex], we get
[tex]y=\dfrac{1}{2}(4)+8[/tex]
[tex]y=2+8[/tex]
[tex]y=10[/tex]
This equation does not contain the point (4,12).
In option C, the given equation is:
[tex]y=-\dfrac{1}{2}x+14[/tex]
Putting [tex]x=4[/tex], we get
[tex]y=-\dfrac{1}{2}(4)+14[/tex]
[tex]y=-2+14[/tex]
[tex]y=12[/tex]
This equation contains the point (4,12).
In option D, the given equation is:
[tex]y=\dfrac{3}{4}x+9[/tex]
Putting [tex]x=4[/tex], we get
[tex]y=\dfrac{3}{4}(4)+9[/tex]
[tex]y=3+9[/tex]
[tex]y=12[/tex]
This equation contains the point (4,12).
Only the equation in option B does NOT contain the point (4,12). Therefore, the correct option is B.
