Point Gradient Formula

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 = $\frac{rise}{run}$.

 

 

m = point gradient of a line.

The formula is:

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

Solved Example

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

Solution:

Given,

$\left( x_{1},y_{1}\right )$ = (–1, –5)

m = 4

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

This is the required equation.

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