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# How do you graph $y=3x+5$?

Last updated date: 12th Aug 2024
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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.

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.