Help your students prepare for their Maths GCSE with this free gradient of a line worksheet of 30+ questions and answers
The gradient of a line tells us how steep that line is, the bigger the gradient, the steeper the line. A line with a positive gradient slopes upwards from left to right and a line with a negative gradient slopes downwards. When the equation of a straight line is written in the form y=mx+c, the value m is the gradient of the line. Straight line graphs are also known as linear graphs as their equations contain terms in x,y and constants only, with no higher powers of x or y.
The gradient of a straight line can be calculated by taking any two points on the line, subtracting the y values, subtracting the x values and then dividing them.
Since the gradient of a line tells us how steep the line is, parallel lines have equal gradients. The gradients of perpendicular lines – lines which meet at right angles – are negative reciprocals of each other.
Horizontal and vertical lines have slightly adapted equations. Lines of the form y=a (where a is a constant) are straight horizontal lines with a gradient of 0. Lines of the form x=a (where a is a constant) are straight vertical lines and have a gradient of ∞.
When drawing straight line graphs, we can either use a table of values calculated using the equation of the line, or we can use information about the y intercept and the gradient of the line. The y intercept tells us the y coordinate of the point where the line crosses the y axis and the gradient tells us how many steps to go up for every one we go across. We can start drawing our line from the given point on the y axis and move across and up/down by the appropriate amount between each point on the line.
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