Question

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

Answer 1

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.