Equation of a line

Slope of a line between coordinates $\text{a}(x_1,y_2)$ and $\text{b}(x_2,y_2)$

$$m=\frac{y_2-y_1}{x_2-x_1}$$

Point-slope form For an arbitrary point $\text{b}(x,y)$

$$m=\frac{y-y_1}{x-x_1}$$ $$\boxed{y-y_1=\text{m}(x-x_1)}$$

Slope-intercept form At $x=0$

$$\boxed{y=\text{m}\cdot x+c}$$

where, $c\rightarrow$ is the $y$ intercept at $x=0$

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References

1. Derivation of the equation of a line | Mathbytes
2. https://www.mathsisfun.com/equation_of_line.html