Answer

Verified

389.1k+ views

**Hint:**For plotting a graph we need different x values as well as their corresponding y values. Such that to solve this question we need to find the x intercept, y intercept and some intermediate values. Also the x- intercept and y-intercept can be found by substituting y=0 and x=0 respectively. After finding these values we just need to plot them on the XY plane.

**Complete step by step solution:**

Given

$y - 6 = 3\left( {x - 4} \right).......................\left( i \right)$

Now we need to find the x intercept, y intercept and some intermediate values for plotting the graph.

X intercept is the point where the graph touches X axis such that y=0, such that substituting y=0 in (i):

\[

\Rightarrow y - 6 = 3\left( {x - 4} \right) \\

\Rightarrow 0 - 6 = 3\left( {x - 4} \right) \\

\Rightarrow 0 - 6 = 3x - 12 \\

\Rightarrow 3x = 12 - 6 \\

\Rightarrow x = \dfrac{6}{3} \\

\Rightarrow x = 2.................\left( {ii} \right) \\

\]

\[\therefore {\text{x intercept}} = \left( {2,0} \right)\]

Now we need to find y intercept:

So we have to put x=0 in (i) since y intercept is the point where the graph touches the Y axis.

$

\Rightarrow y - 6 = 3\left( {x - 4} \right) \\

\Rightarrow y - 6 = - 12 \\

\Rightarrow y = - 12 + 6 \\

\Rightarrow y = - 6..................\left( {iii} \right) \\

$

\[\therefore y{\text{ intercept}} = \left( {0, - 6} \right)\]

Now let’s find some intermediate points:

For x=1:

$

\Rightarrow y - 6 = 3\left( {x - 4} \right) \\

\Rightarrow y - 6 = 3\left( {1 - 4} \right) \\

\Rightarrow y - 6 = 3\left( { - 3} \right) \\

\Rightarrow y = - 9 + 6 \\

\Rightarrow y = - 3 \\

$

$\therefore \left( {1,\; - 3} \right)\;{\text{is}}\;{\text{a}}\;{\text{point}}{\text{.}}$

For x=3

\[

\Rightarrow y - 6 = 3\left( {x - 4} \right) \\

\Rightarrow y - 6 = 3\left( {3 - 4} \right) \\

\Rightarrow y - 6 = 3\left( { - 1} \right) \\

\Rightarrow y - 6 = - 3 \\

\Rightarrow y = - 3 + 6 \\

\Rightarrow y = 3 \\

\]

\[\therefore \left( {3,\;3} \right)\;{\text{is}}\;{\text{a}}\;{\text{point}}{\text{.}}\]

Now all these values which we have got from above is to be plotted in a XY plane.

Plotting the points

\[\left( {2,0} \right),\left( {0, - 6} \right),\left( {1, - 3} \right),\left( {3,3} \right)\]

On plotting the above points we get the following graph:

**The above graph shows the plot of$y - 6 = 3\left( {x - 4} \right)$ .**

**Note:**

While approaching similar graphical questions one should find as many points as possible from the given conditions and common knowledge. Also one must be careful while doing the solution. Also while plotting the graph one must choose appropriate scale considering the values that should be plotted such that our every value can be represented on the graph.

Recently Updated Pages

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Advantages and disadvantages of science

10 examples of friction in our daily life

Trending doubts

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Which are the Top 10 Largest Countries of the World?

Give 10 examples for herbs , shrubs , climbers , creepers

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

10 examples of law on inertia in our daily life

Write a letter to the principal requesting him to grant class 10 english CBSE

Difference Between Plant Cell and Animal Cell

Change the following sentences into negative and interrogative class 10 english CBSE