How do you find the gradient of a line on a graph?

I have my line of best fit and I need to find its gradient


Can anybody help me out please and explain clearly otherwise I'll just get confused! Thanks!How do you find the gradient of a line on a graph?
Take any two points on the line. Choose the most convenient.





The gradient is the slope of the line, which as it's straight, is the same everywhere, and the slope or gradient is the same as the tangent. To calculate this, take your two points, then work out ';the differences of the Ys divided by the difference of the Xs';.





If you drop a vertical line from the upper point, and draw a horizontal through the lower point, you'll see you've formed a right-angled triangle, with the slope as the hypotenuse. You've just calculated the tangent of the slope (';opposite over adjacent';, using the standard names of the sides).How do you find the gradient of a line on a graph?
Draw a line vertically down from your line of best fit to the x-axis, forming a right-angled triangle between the x-axis, your line of best fit and the line you just drew. Measure the length of this line (remembering the scale of the y-axis) and divide that by distance from the origin to the point where the line you drew meets the x-axis (remembering the scale of the x-axis) and the result will be the gradient of your line of best fit. Generally, the bigger the triangle, the more accurate your result for the gradient will be.





By ';remember the scale';, I mean that if each cm on the x-axis represented 100, and each cm on the y-axis represented 1000, then remember to take that into account when calculating your gradient - if the line you drew down to the x-axis was 5cm long and the distance from origin to meeting point was 3cm, then it wouldn't just be 5/3, it would be 5000/300, or 50/3.
Take the co-ordinate of the highest part (x1,y1) where x1 and y1 are the co-ordinates.





Take the co-ordinates of the lowest part of the line, or the other end (x2,y2)





then uses this formula for the gradient.





the gradient M=(y2-y1)/(x2-x1)





and bobs ur uncle!


if the line slopes down from left to right then the gradient M will be negative. If the line slopes upwards from left to right the gradient is positive.





alternatively google it!
A straight line can be described by an equation of the form


y = a + bx





To find the value of a you need to set x to 0 (think about it!). This means that a is the value of y where the line crosses the y axis (i.e. where x=0).





Now you have a you can work out the rest easily. Choose the point on the line where x is, say, 10. So y = a + 10b. You already know a (see above) so just find out what y is from your graph and plug it into the equation. Then you'll have b too.





Job done.