 2023-02-24

How to graph $y=4x+3$ using a table? Quincy Doyle

Consider it like this: You plug in something for $x$, and you follow the expression $4x+3$ by multiplying by $4$ then adding $3$, to get the corresponding output value $y$.
This equation is linear: $y=mx+b$,
where $m$ is the slope (change in y over change in x) and $b$ is the y-intercept (where it hits the $y$ axis).

Your equation just has $m=4$ and $b=3$.
So, let's make a quick table. You need at least two points to make a straight line, and three points to make a curve. Let's do five points though for practice.

$x=-2\to y=4\left(-2\right)+3=-5$
$x=-1\to y=4\left(-1\right)+3=-1$
$x=0\to y=4\left(0\right)+3=3$
$x=1\to y=4\left(1\right)+3=7$
$x=2\to y=4\left(2\right)+3=11$

In a table it then looks like this:

$\left[\begin{array}{ccc}\underline{y}& \underline{\text{|}}& \underline{x}\\ -5& \mid & -2\\ -1& \mid & -1\\ 3& \mid & 0\\ 7& \mid & 1\\ 11& \mid & 2\end{array}\right]$

And after plotting each point by looking at $x$ and $y$, and moving to the right $x$ units and up $y$ units (if negative, move the opposite direction), we get:
graph{4x + 3 [-2, 2, -5, 11]}
Every point we put on the table should be visible if you look at this graph.

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