How do you graph y=4x+3y=4x+3 using a table?

1 Answer
Jan 10, 2017

Well, think of it this way: you plug in something for xx, and you follow the expression 4x + 34x+3 by multiplying by 44 then adding 33, to get the corresponding output value yy.

This equation is linear: y = mx + by=mx+b,

where mm is the slope (change in y over change in x) and bb is the y-intercept (where it hits the yy axis).

Your equation just has m = 4m=4 and b = 3b=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 -> y = 4(-2) + 3 = -5x=2y=4(2)+3=5
x = -1 -> y = 4(-1) + 3 = -1x=1y=4(1)+3=1
x = 0 -> y = 4(0) + 3 = 3x=0y=4(0)+3=3
x = 1 -> y = 4(1) + 3 = 7x=1y=4(1)+3=7
x = 2 -> y = 4(2) + 3 = 11x=2y=4(2)+3=11

In a table it then looks like this:

color(white)([(color(black)(ul(y)),color(black)(ul("|")),color(black)(ul(x))),(color(black)(-5),color(black)(|),color(black)(-2)),(color(black)(-1),color(black)(|),color(black)(-1)),(color(black)(3),color(black)(|),color(black)(0)),(color(black)(7),color(black)(|),color(black)(1)),(color(black)(11),color(black)(|),color(black)(2))])

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]}

If you look on this graph, you should be able to find every point we had on the table.