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Draw the graph of the equation $2x + 3y = 12$. From the graph find the co-ordinates of the point whose y-coordinates is $3$.
Given:
Given equation $2x + 3y = 12$.
To do:
We have to draw the graph and find the co-ordinates of the point whose y-coordinates is $3$.
Solution:
To represent the above equation graphically we need at least two solutions for the given equation.
For equation $2 x+3 y=12$
$2x=12-3 y$
$x=\frac{12-3 y}{2}$
If $y=0$, then
$x=\frac{12-3 \times 0}{2}$
$=\frac{12-0}{2}$
$=\frac{12}{2}$
$=6$
If $y=4$, then
$x=\frac{12-3 \times 4}{2}$
$=\frac{12-12}{2}$
$=\frac{0}{2}$
$=0$
$x$ | $0$ | $6$ |
$y$ | $4$ | $0$ |
Plot the points $A(0, 4)$ and $B6, 0)$ on the graph and join them to get the graph of the given equation.
The above situation can be plotted graphically as below:
If $y = 3$, then,
Draw a perpendicular from $y = 3$ on the line to the X-axis which meets it at $C$ then x-coordinate of $C$ is $\frac{3}{2}$.
Therefore,
The coordinates of $C$ are $(\frac{3}{2}, 3)$.