[Math] Functions: Linear Function: $f(x) = 3x + 5.$

functions

Hey if i wanted to get a linear function how would i do it? Im being shown an example and the results are supposedly:

x   3x+5
-2  -1
-1  2
0   5
1   8
2   11

But i cant figure out how to get it.
The equation is $f(x) = 3x + 5.$

And i need to plot it on the graph. Can anyone help?

Best Answer

The general equation for a straight line in Cartesian co-ordinates is $y=mx+c$, where $m$ is the gradient of the straight line and $c$ is the y-intercept of the line.

In the case of your line $f(x)$, you have $m=3$, $c=5$. So you have a straight line which passes through the point $(0,5)$ and has gradient $3$, this means you can plot a graph like that shown below (note we can calculate the x-intercept as $(-\frac{5}{3},0)$ by setting $f(x)=0$):

Graph of f(x)

Hope this helps!

note:corrected the x-intercept to (-5/3,0)

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