Math Is Fun Forum

paulb203

Member

Registered: 2023-02-24

Posts: 136

"Values" gradient v "grid" gradient

I’ve just completed a straight line graph for the equation y=4x-4.

y=mx+c tells me that the gradient(m)is 4 (and the y intercept is -4)

But the y values on the grid go up in 2s (2,4,6,8, etc) with 1 grid square for each value of 2. Whereas the x values on the grid go across in 1s (1,2,3) with two grid squares for each value of 1.

So the straight line graph on the grid looks like a y=x graph, with a gradient of 1, a line of 45 degrees, even though the gradient according to the values is 4, and would therefore be steeper, if drawn to scale.

I’m pretty sure the values on the grid were marked out this way due to the restriction of the page size (the y values went up to 16 and down to -12, so to give a whole square to the value of 1 would take up too much space vertically). But the x values only went from -2 to 3 so space wasn't an issue there.

So why don’t they do the grid to scale, where possible, which would make the line, and therefore the gradient, to scale? I think this would help the novice student grasp the steepnees of lines relative to various equations etc, and get the hang of graphs that appear frequently in maths.

I redrew the grid giving the x values 1 square for every value of two, like the y values to square ratio, and, for me, it looks better, and feels right. The other way just looks, and feels 'wrong'.

Also, just double checking on the difference between the grid and the graph. The grid is the thing we’re presented with on the page, the thing we have in front of us before we start drawing little dots or crosses on, before we draw a line through them; and the graph is the line itself, yeah? Or is the whole completed thing the graph?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,167

Re: "Values" gradient v "grid" gradient

hi paulb203,

What graph plotter were you using?

Try this https://www.mathsisfun.com/data/function-grapher.php

This has equally scaled axes so a steep line looks steep.

Not sure if you can change the scales with it. You can in Excel.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

paulb203

Member

Registered: 2023-02-24

Posts: 136

Re: "Values" gradient v "grid" gradient

Thanks, Bob.

What plotter was I using? I've never used one, nor seen one, until now

I was using some printed out exercise pages.

I tried your plotter; great stuff. I'll use that from now on