The ratio of vertical change to horizontal change of a line is defined by point gradient. A gradient is also known as a derivative. The gradient of a line is m =

\begin{array}{l} \frac{r i s e}{r u n} \end{array}

m = point gradient of a line.

The formula is:

$m = \frac{y - y_{1}}{x - x_{1}}$

Solved Example

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

Solution:

Given,

\begin{array}{l} (x_{1}, y_{1}) \end{array}

= (–1, –5)

m = 4

Point Gradient Formula:

\begin{array}{l} y - y_{1} = m (x - x_{1}) \end{array}

\begin{array}{l} y - (- 5) = 4 (x - (- 1)) \end{array}

\begin{array}{l} y + 5 = 4 (x + 1) \end{array}

y = 4x + 4 – 5
y = 4x – 1

This is the required equation.

Solved Example

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