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What you need to know
What you need to know:
The gradient of a graph is a measure of how steep it is. If the gradient is small, the slope of the line will be very gradual, but if the gradient is big, the line will be quite steep. You are required to know how to calculate the gradient from two possible circumstances:
- You are given the line drawn on a graph;
- You are given two coordinates and told that a line passes through both.
These situations may seem distinct, but they aren’t really. If in the first situation you choose two coordinates on the line, then it immediately becomes precisely the second situation. Gradient is measured by considering how much the y values change in comparison to the x values. In either case, the process amounts to dividing the “change in y” by the “change in x”.
y = mx + c
Any straight line can be expression by the equation y = mx + c.
In this equation, x and y represent the coordinates – the two axis on the graph – whilst the m represents the gradient, and c represents the y-intercept (where the line meets the y-axis).
You are expected to be able to both draw a straight line given the equation (sometimes the equation is not given exactly in this form and will require some algebraic rearranging), and determine the equation of a straight line given information about it. For the latter you must firstly determine the gradient, and then from there you can substitute the value of the gradient, along with any coordinates (x, y) which the line passes through, either directly into the equation y = mx + c to find the y-intercept, or into the equation:
y - y_1 = m(x - x_1)
This will directly produce the straight line equation, so all that remains is to rearrange into the form y = mx + c if the question asks you to do so.
Gradients of Straight Line Graphs Revision and Worksheets
For those teachers or tutors looking for new resources for the GCSE maths 9-1 course you will find our gradient of a straight line worksheets useful for things like homework and classwork. If you are interested in other GCSE Maths resources visit our main page.
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