Question

Draw the graph of the linear equation 3x+4y=6.

And answer the following questions:

a) At what points does the graph cut the x axis and y axis

b) Find area enclosed by the line and both the axes.​

Answer 1

Step-by-step explanation:

Refer the attachment for graph.

Equation given : 3x + 4y = 6

$\sf{\longrightarrow} \: 3x + 4y = 6$

$\sf{\longrightarrow} \: 3x= 6 - 4y$

$\sf{\longrightarrow} \:x = \dfrac{6 - 4y}{3}$

• When y = 0

$\sf{\longrightarrow} \:x = \dfrac{6 - 4(0)}{3} = \dfrac{6}{3}$

$\sf{\longrightarrow} \:x = 2$

• When y = 3

$\sf{\longrightarrow} \:x = \dfrac{6 - 4(3)}{3} = \dfrac{ - 6}{3}$

$\sf{\longrightarrow} \:x = - 2$

• When y = 6

$\sf{\longrightarrow} \:x = \dfrac{6 - 4(6)}{3} = \dfrac{ - 18}{3}$

$\sf{\longrightarrow} \:x = - 6$

Solutions for 3x + 4y = 6,

$\begin{tabular}{|c|c|c|c|}\cline{1-4} x&2&-2&-6\\\cline{1-4}\ y&0&3&6\\\cline{1-4}\end{tabular}$

(If you're a app user, kindly refer the attachment)

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Question a)

The graph cuts x-axis at (2,0) and y-axis at (0,1.5)

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Question b)

There is a triangle formed.

$\sf{Area \: of \: Triangle = \frac{1}{2} \times Base \times Height}$

Base = 2 units

Height = 1.5 units

$\sf{\longrightarrow} \: \dfrac{1}{2} \times 2 \times 1.5$

$\sf{\longrightarrow} \: 1 \times 1.5$

$\sf{\longrightarrow} \:1.5 \: sq. \: units$

Area of the enclosed figure is 1.5 sq. units.

Answer 2

Given

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• Linear equation 3x + 4y = 6.

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What to do

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• Draw graph of given equation.

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To Find

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• At what points does the graph cut the x axis and y axis?

• Area enclosed by the line and both the axes?

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Solution

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• Putting x = 0 in given equation :

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➥ 3(0) + 4y = 6

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➥ (3 × 0) + 4y = 6

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➥ 0 + 4y = 6

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➥ 4y = 6

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➥ y = $\sf {\cancel{\dfrac{6}{4}}}$

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➥ y = 1.5

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➥ (0, 1.5)

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• Putting y = 0 in given equation :

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➥ 3x + 4(0) = 6

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➥ 3x + (4 × 0) = 6

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➥ 3x + 0 = 6

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➥ 3x = 6

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➥ x = $\sf {\cancel{\dfrac{6}{3}}}$

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➥ x = 2

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➥ (2, 0)

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• Plotting the points on graph!

• Refer the attachment for graph.

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✇ Answers for (a) and (b) :

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(a)

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• Graph will cut x axis at (2, 0) and y axis at (0, 1.5).

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(b)

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• As from graph we can understand that enclosed area is right angled triangle, it's area is given by ½ × B × H, where B is base of triangle and H is height of triangle. We have B = 2 units and H = 1.5 units.

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• Putting all values in the formula :

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➦ Area = ½ × 2 × 1.5

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➦ Area = 1 × 1.5

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➦ Area = 1.5

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• Therefore, area enclosed by the line and both the axes is 1.5 sq.units.

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Know More

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• Linear equation is an equation between two variables.

• It gives a straight line when we plot it on graph.

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