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# How do you graph $y = 2x + 3$?

Last updated date: 12th Jul 2024
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Hint: In the given question, we have been given an equation in two variables. We have to plot the line on a graph that forms from this equation. To do that, we first convert the given equation to slope-intercept form. From there, we find out the value of slope and the y-intercept. We plot a point at the y-intercept on the y-axis. From there, we move up or down and then right or left depending upon the coefficient of $x$ and $y$ respectively and join the points to form the line.

Formula Used:
The standard form of a linear equation in slope-intercept form is:
$y = mx + b$

Complete step by step solution:
The given equation is $y = 2x + 3$.
Clearly, this equation is of the type $y = mx + b$, hence, is already in the slope-intercept form.
Thus, slope $m = 2$
And y-intercept $b = 3$
Hence, one point on the graph can be taken as $\left( {0,3} \right)$.
Now,
$m = \dfrac{{coefficient{\text{ }}of{\text{ }}x}}{{coefficient{\text{ }}of{\text{ }}y}} = \dfrac{{run}}{{rise}}$
Hence, we move up $1$ (coefficient of $y$) points and then move to the right $1$ (coefficient of $x$) points.
Thus, the second point is $\left( {0 + 1,3 + 2} \right) = \left( {1,5} \right)$.
Now, we plot the two points and join them, and we have our line.

The meaning of slope is run divided by rise, i.e., $\dfrac{{coefficient{\text{ }}of{\text{ }}x}}{{coefficient{\text{ }}of{\text{ }}y}}$.