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

$x=\frac{12-3 \times 4}{2}$

$=\frac{12-12}{2}$

$=\frac{0}{2}$

$=0$

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 $(\frac{3}{2}, 3)$.

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Updated on: 10-Oct-2022

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