Answer

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**Hint:**The above given equation is the equation of a straight line because the power of variables is $1$. This equation of straight line can be compared with the general equation $y=mx+c$. Here, $m$ is a slope of line and $c$ is called as $y-$intercept for this particular equation.

**Complete step by step solution:**It is given in the question that $y=3x+5$ comparing the above equation with slope – intercept of equation i.e.$y=mx+c$

Therefore, the slope $m=3$ and $y-$intercept of equation $(c)=5$

For drawing the graph of the above equation we need any two points.

Therefore, selecting any two random values of $x$ and we will find corresponding value of $y$

For equation $y=3x+5$

For

$x=0$

$y=3\times 0+5$

$y=5$

First point is \[\left( 0,5 \right)\]

For

$x=1$

$y=3\times 1+5$

$y=8$

Second point is \[\left( 1,8 \right)\]

Drawing table for \[x\] and \[y\]

$x$ | $0$ | $1$ |

$y$ | $5$ | $8$ |

The above graph is the graph at equation $y=3x+5$

Here, the straight line which we have got is a never ending line .If you provide values it will move up to infinity in positive as well as in negative direction.

**Additional Information:**

For the equation similar to \[y=mx+c\] there are a number of ways other than conventional ways of drawing graphs.

For example: \[y=2x+5\]

Here, the y – intercept \[(c)=5\] and slope \[m=2\]

Therefore slope \[m\] is also \[\tan \theta \]

\[\therefore \tan \theta =2\]

\[\theta ={{\tan }^{-1}}(2)\]

\[\theta =63.43\]

Taking point \[5\] on \[y\] - axis and calculating angle \[63.43\] from \[x\] - axis and drawing a straight line we will get the graph.

You can also convert this equation in point slope form to equation.

\[y=3x+5\]

\[y-5=3(x-0)\]

Comparing it with point slope form of equation

\[y-{{y}_{1}}=m(x-{{x}_{1}})\]

Point \[({{x}_{1}},{{y}_{1}})\equiv (0,5)\] and slope \[m=3\]

**Note:**

When drawing a graph, take the values properly on the right axis and do not misplace the values of \[x\] and \[y\] - axis.

In solution you can take any random values for \[x\] to find \[y\] but make sure to take \[x=0\] because if it is not taken that there is no point of finding \[y\] - intercept for the question.

Join the points properly and with the help of scale do not join the point free handed as it is a straight line equation.

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