Question

How do you find slope with two variables?

Answer 1

Finding slope with two variables:

Let $\alpha x+\beta y+\gamma =0$ be the equation of a line with two variables $x$ and $y$.

Now,

$\beta y=-\alpha x–\gamma =0$

$\Rightarrow$ $y=\left(\frac{-\alpha }{\beta }\right)x–\left(\frac{\gamma }{\alpha }\right)$

This is of the form $y=mx+c$, where $m$ is the gradient or slope of the line and $c$ is the y-intercept.

Therefore, slope $=m$

$=-\frac{\alpha }{\beta }$

Suppose a line passes through the points $(x_1,y_1)$ and $(x_2,y_2)$, then the slope of the line is given by:

$\mathit{m}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{(}{\mathbf{y}}_{\mathbf{2}}\mathbf{}\mathbf{–}\mathbf{}{\mathbf{y}}_{\mathbf{1}}\mathbf{)}}{\mathbf{(}{\mathbf{x}}_{\mathbf{2}}\mathbf{}\mathbf{–}\mathbf{}{\mathbf{x}}_{\mathbf{1}}\mathbf{)}}$

Hence, we can find the slope with two variable by the formula $\mathit{m}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{(}{\mathbf{y}}_{\mathbf{2}}\mathbf{}\mathbf{–}\mathbf{}{\mathbf{y}}_{\mathbf{1}}\mathbf{)}}{\mathbf{(}{\mathbf{x}}_{\mathbf{2}}\mathbf{}\mathbf{–}\mathbf{}{\mathbf{x}}_{\mathbf{1}}\mathbf{)}}$.