Easy
Solve the equation $2y + 1 = y + 4$ and represent the solution$(s)$ on $(1)$ the number line $(2)$ the Cartesian plane.
(A) We solve the equation $2y + 1 = y + 4$:
$\therefore 2y - y = 4 - 1$
$\therefore y = 3$
$(1)$ Representation on the number line:
Since $y = 3$ is an equation in one variable,it represents a unique point on the number line at the position $3$.
$(2)$ Representation on the Cartesian plane:
We know that $y = 3$ can be written as a linear equation in two variables: $0x + 1y = 3$.
For any value of $x$,the value of $y$ remains $3$. Thus,we can choose points like $(0, 3)$,$(1, 3)$,and $(3, 3)$. Plotting these points on the Cartesian plane and joining them results in a line parallel to the $x$-axis passing through $y = 3$.
$\therefore 2y - y = 4 - 1$
$\therefore y = 3$
$(1)$ Representation on the number line:
Since $y = 3$ is an equation in one variable,it represents a unique point on the number line at the position $3$.
$(2)$ Representation on the Cartesian plane:
We know that $y = 3$ can be written as a linear equation in two variables: $0x + 1y = 3$.
For any value of $x$,the value of $y$ remains $3$. Thus,we can choose points like $(0, 3)$,$(1, 3)$,and $(3, 3)$. Plotting these points on the Cartesian plane and joining them results in a line parallel to the $x$-axis passing through $y = 3$.
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