Question

Draw the graph of the equation given below.Also find the coordinates of the points where the graph at the coordinates axes.
3x+2y-6=0​

Answer 1

$\underline\green{\bold{Given \: Question :- }}$

• Draw the graph of the equation given : 3x+2y-6=0
• Also find the coordinates of the points where the graph at the coordinates axes.

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$\huge \blue{AηsωeR} ✍$

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$\bf \:The \: equation \: of \: line \: is \: 3x+2y-6=0$

☆ can be rewritten as  3x + 2y = 6

➣ To calculate the coordinates of points, which are lies on the line, are shown in the below table.

$\begin{gathered}\boxed{\begin{array}{cccc}\bf x & \bf y \\ \frac{\qquad \qquad \qquad \qquad}{} & \frac{\qquad \qquad \qquad \qquad}{} \\ \sf 0 & \sf 3 \\ \\ \sf 2 & \sf 0 \end{array}} \\ \end{gathered}$

$\bf \:↝ For \: graph \: see \: the \: attachment.$

$\begin{gathered}\begin{gathered}\bf So = \begin{cases} &\bf{Iine \: cut \: the \: x- axis \: at \: (2,0)} \\ &\bf{line \: cut \: the \: y - axis \: at \: (0,3)} \end{cases}\end{gathered}\end{gathered}$

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$\large \red{\bf \: ⟼ Explore \: more } ✍$

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How to represent a graph of linear equation in two variables?

• Linear equation in two variables is represented graphically by the line whose points give the collection of solutions of the equation. This is called graphing linear equation.

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Properties for graphing linear equation:

• 1. Linear equations have infinitely many solutions.
• 2. Every point (h, k) on the line AB gives the solution x = h and y = k.
• 3. Every point which lies on AB satisfies the equation of AB.
• 4. To draw an exact line on the graph paper you can plot as many points you like, but it is necessary to plot minimum three points.

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Note:

• 1. Linear equation in two variables has infinitely many solutions.
• 2. A graph of linear equation is always a straight line.
• 3. Every point on the straight line is the solution of the linear equation.
• 4. Equation of y-axis is x = 0. The standard form of this equation is x + 0.y = 0.
• 5. Equation of x-axis is y = 0. The standard form of this equation is 0.x + y = 0.
• 6. x = a is a graph of straight line parallel to y-axis and standard form of this equation is x + 0.y = a
• 7. y = b is a graph of straight line parallel to x-axis and standard form of this equation is 0.x + y = b.
• 8. The equation y = mx is always passing through the origin (0, 0)

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