Draw the graph of linear equation 3x 4y 12

Asked by admin @ 23/08/2021 in Math viewed by 341 People

Draw the graph of the equation 3x + 4y = 12 and find the coordinates of the points of intersection where the graph intersects coordinate axes. Check from the graph that (-4,6) is a solution of the equation

Answered by admin @ 23/08/2021

Gɪᴠᴇɴ :

Linear equation,

$\begin{gathered}\bf\blue{3x\:+ \: 4\:y\:=\:12} \\ \end{gathered}$

❶ Substituting 'x = 0' in the given equation, we get

$\begin{gathered}:\implies\:\:\sf{3\times{0}\:+ \: 4\:y\:=\:12} \\ \end{gathered}$

$\begin{gathered}:\implies\:\:\sf{0\:+ \: 4\:y\:=\:12} \\ \end{gathered}$

$\begin{gathered}:\implies\:\:\bf{y\:=\:3} \\ \end{gathered}$

❷ Substituting 'x = 2' in the given equation, we get

$\begin{gathered}:\implies\:\:\sf{3\times{2}\:+ \: 4\:y\:=\:12} \\ \end{gathered}$

$\begin{gathered}:\implies\:\:\sf{6\:+ \: 4\:y\:=\:12} \\ \end{gathered}$

$\begin{gathered}:\implies\:\:\sf{\: 4\:y\:=\:12 \: - \: 6} \\ \end{gathered}$

$\begin{gathered}:\implies\:\:\sf{\: 4\:y\:=\:6} \\ \end{gathered}$

$\begin{gathered}:\implies\:\:\bf{y\:=\:1.5} \\ \end{gathered}$

❸ Substituting 'y = 0' in the given equation, we get

$\begin{gathered}:\implies\:\:\sf{4\times{0}\:+ \: 3\:x\:=\:12} \\ \end{gathered}$

$\begin{gathered}:\implies\:\:\sf{0\:+ \: 3\:x\:=\:12} \\ \end{gathered}$

$\begin{gathered}:\implies\:\:\bf{x\:=\:4} \\ \end{gathered}$

Hᴇɴᴄᴇ,

➢ Pair of points of the given equation are shown in the below table.

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf 3 \\ \\ \sf 2 & \sf 1.5 \\ \\ \sf 4 & \sf 0 \end{array}} \\ \end{gathered}$

➢ Now draw graph using the points (0 , 3), (2 , 1.5) & (4 , 0)

➢ See the attachment graph.

☆ Hence, (- 4, 6) lies on the graph.

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