how do you find the gradient?

Question

y=x+2
the gradient in this simple formulae is 1, but how do you find it?

so in the formulae y=2x+3 the gradient is 2

Answer 1

In any graph of the form
y = ax + b
(i.e. any straight line)
The gradient is a.

Where functions or higher powers of x are used, the gradient will also be a function of x.

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Yes, it's 2 in your second example.
As jphelps says, "gradient" is just the change in y for a unit change in x, so take any two points on the line and calculate
(difference in y) / (difference in x)

Any other type of equation produces a line that isn't straight, which means the gradient varies as x changes, so you won't be able to state a number for the gradient without stating which x you're looking at, and also you can't use two arbitrary points to calculate gradient - you need to get into clever stuff called "differential calculus".

Answer 2

The gradient is the slope of the line.

One way to think about a measure of the slope is, how many units does y change by for each unit change in x. The higher the gradient, the steeper the line.

If x increases by 1, how much does y increase by?

In this case, 1 is the gradient.

If y = 2x+1, the gradient would be 2.

If you think about the line as the side of a mountain, how steep is it? If the gradient is 2, then you will rise 2meters for every 1meter you step forward.

Answer 3

The gradient can be thought of as the slope of the line. If you are familiar with slope intercept form (y=mx+b, where m represents the slope, or gradient and b represents the y intercept) you can easily see this equation is in that form and m=1.

If you are not familar with slope intercept form, you can simply take two points on the line and calculate the slope from the two points.

Take the values x=1 and x=2. By plugging them into the equation, you can arrive at the coordinate pairs (1,3) and (2,4).

If we calculate the slope between them, we just take the change in y divided by the change in x.

(4-3)/(2-1)=1

Therefore the gradient is 1.

Answer 4

The equation of a sraight line is given by:-
y=mx+c gradient m , passes thro` (0,c)
Examples are:-
y=1x + 2 gradient 1,passes thro` (0,2)
y=5x + 4 gradient 5,passes thro` (0,4)
y=7x + 6 gradient 7,passes thro` (0,6)
The gradient is therefore the number in front of x.
Hope this helps.

Answer 5

The gradient of a line is the change in y over the change in x ie.
y2 - y1 (change in y) / x2 - x1 (change in x)

This gives the m value in : y = mx + c

To work this out you can just put in values (ie x=1 and x=2 to see the change), but for more difficult ones you will need to differentiate (see other posts for this)

ie. dy/dy = na x ^n-1
= 1 (in this case)

Answer 6

For any straight line, described by the formula y=mx + c:

The gradient is m. Simple as that. It tells us how "steep" the line is.
The "c" bit tell you how far up or down the y axis you go.

If you need to graph it, you find it by "rise over run".