# Functions: Linear Function: $f(x) = 3x + 5.$

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?

-

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 $f(x)=0$):

Hope this helps!

-

As Shaktal points out "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."

So you need to find the gradient or slope 'm' and the y-interecpt 'c', in other words the value of y where x=0.

To find the gradient, since the equation is linear, you can take any two points (a, b) and (c, d) and calculate

(d-b)
-----=m
(c-a)


Then once you have that number m, you can take any point (x, y) and write y=mx+c. Then you can figure out the value of c such that this equation holds true.

As an example say you have (1, 4) and (2, 10) as the points for which you want to find a linear equation. m=(6/1)=6. Then considering (2, 10) we can write 10=(6)(2)+c or 10=12+c. So, c=-2, and our linear equation reads y=6x-2.

If you hand-plot the points, draw out your co-ordinate system, plot the points, and then connect them with a ruler or straight edge.

-