The gradient
The In a graph, the gradient is the steepness of the line. The greater the gradient, the greater the rate of change. tells us how steep a line is, therefore the bigger the gradient the steeper the line is.
A positive gradient is a straight line which slopes up to the right.
A negative gradient is a straight line which slopes down to the right.
Gradients of special types of lines
Parallel lines have the same gradient
Vertical lines have a gradient which is undefined
Equation \(x = a\)
Horizontal lines have a gradient of zero
Equation \(y = b\)
One of the formulae used to find the gradient of a straight line is:
\(Gradient\,of\,a\,slope = \frac{{vertical\,distance}}{{horizontal\,distance}}\)
Now try some example questions.
Question
The community centre is getting a new ramp onto their side entrance.
Calculate the gradient of the ramp using the diagram below.
The gradient can be worked out as a simplified fraction or a decimal fraction. Gradient is positive since the line slopes up to the right.
\(Gradient = \frac{{vertical\,distance}}{{horizontal\,distance}}\)
\(= \frac{{26}}{{78}}\)
\(=\frac{13}{39}\)
\(=\frac{1}{3}\)
or
\(= 26 \div 78\)
\(= 0.333...\)
\(= 0.3\,(to\,1\,d.p.)\)
Question
Calculate the gradient of the line shown below.
Gradient is negative since the line slopes down to the right.
\(Gradient\, = \frac{{vertical\,distance}}{{horizontal\,distance}}\)
\(-\frac{5}{2}\)
Question
Calculate the gradient of the slope below.
Gradient is negative since the line slopes down to the right.
\(Gradient\, = \frac{{vertical\,distance}}{{horizontal\,distance}}\)
\(= \frac{{ - 5}}{{20}}\)
\(= - 5 \div 20\)
\(= - 0.25\,(to\,2\,d.p.)\)
Question
Calculate the gradient of the slope below.
Gradient is positive since the line slopes up to the right.
\(Gradient\, = \frac{{vertical\,distance}}{{horizontal\,distance}}\)
\(= \frac{{10}}{{45}}\)
\(= \frac{2}{9}\)
