How do you graph #y=6x-3# by plotting points?

2 Answers

Answer:

Plug in random values for #x#, then solve.

Explanation:

For example, let's pick #0#, #1#, and #2#.

#y=6(0)-3= -3#

#y=6(1)-3= 3#

#y=6(2)-3= 9#

Then just plot #(0, -3)#, (#1, 3)#, #(2, 9)# into a graph like so:

graph{y=6x-3 [-15, 15, -5, 10]}

May 8, 2018

Answer:

See below

Explanation:

First of all, note that this function is a polynomial, because it can be written as a sum of powers of a variable with some coefficients:

#p(x) = a_0 + a_1x + a_2x^2 + ... + a_nx^n#

In your case, #n=1#, #a_0=-3# and #a_1=6#

And it is because #n=1# that this function is a line: every polyinomial of degree #1# represents a line.

To draw a line, you only need two points, so that you can connect them. To sample two points from the equation, you need to choose two points #x_1,x_2# and compute the respective images #y_1,y_2#. Then, draw them and connect the points #(x_1,y_1)# and #(x_2,y_2)#

Of course, it makes no sense to choose "difficult" points to compute, since any couple will work. For this reason, you may choose, for example, #x_1=0# and #x_2=1#, so that the computations will be easy:

#x_1=0 \implies y_1 = 6\cdot 0 - 3 = -3 \implies P_1 = (0,-3)#

#x_2=1 \implies y_1 = 6\cdot 1 - 3 = 3 \implies P_2 = (1,3)#

Now you only need to draw #P_1# and #P_2# and connect them.