Emmett Bradley

2023-02-24

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

Quincy Doyle

Beginner2023-02-25Added 8 answers

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.

$x=-2\to y=4(-2)+3=-5$

$x=-1\to y=4(-1)+3=-1$

$x=0\to y=4\left(0\right)+3=3$

$x=1\to y=4\left(1\right)+3=7$

$x=2\to y=4\left(2\right)+3=11$

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.

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.

$x=-2\to y=4(-2)+3=-5$

$x=-1\to y=4(-1)+3=-1$

$x=0\to y=4\left(0\right)+3=3$

$x=1\to y=4\left(1\right)+3=7$

$x=2\to y=4\left(2\right)+3=11$

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.