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Point Gradient Formula

The ratio of vertical change to horizontal change of a line is defined by point gradient. Gradient is also known as derivative. The gradient of a line is $\frac{rise}{run}$

M = point gradient of a line. The formula is:

\[\large m=\frac{y-y_{1}}{x-x_{1}}\]

Solved Examples

Question: Find the equation of the straight line that has slope m = 4 and passes through the point (–1, –5).


$\left( x_{1},y_{1}\right )$=(–1, –5)

Point Gradient Formula: $y – y_1 = m \left( x-x_1 \right )$

$y-(-5) = 4 \left (x-(-1) \right )$
$y + 5 = 4 \left ( x+1 \right )$
y = 4x + 4 – 5
y = 4x – 1

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