Gradients of special types of lines
Parallel lines
Parallel lines have the same gradient.
Vertical lines
Vertical lines have a gradient which is undefined; equation \(x = a\)
Horizontal lines
Horizontal lines have a gradient of zero; equation \(y = b\)
Question
Which of these lines are horizontal and which are vertical?
\(x=3\)
\(y=-6\)
\(y=5\)
\(x=-2\)
Horizontal is \(y=-6\) and \(y=5\)
Vertical is \(x=3\) and \(x=-2\)
Question
Calculate the gradient of the line which passes through the points \( (3, 4)\) and \((7, 12)\).
\((x_{1}, y_{1})\) and \((x_{2}, y_{2})\)
\( (3, 4)\) and \((7, 12)\)
\(m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)
\(=\frac{12-4}{7-3}\)
\(=\frac{8}{4}\)
\(=2\)
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