Question

Explain the Equation $y=mx+c$

Answer 1

STEP 1: Definition

1. The linear equation$y=mx+c$ is an equation of the line with m as slope and $c$as the$y$-intercept. This form of the equation of a line is called the slope-intercept form, and the values of $m$ and $c$ are real numbers.
2. The slope, $m$ represents the steepness of a line. It is also termed a gradient sometimes.
3. The $y$-intercept, $c$ of a line, is the$y$-coordinate of the point at which the graph of the line intersects with the $y$-axis.

STEP 2: Derivation of the equation $y=mx+c$

Let$\mathrm{L}$ be the line intersecting $y$-axis at (0$0$,$c$)

Here the line$\mathrm{L}$ is having a slope $m$ and$y$-intercept $c$

We know the equation of a line in point-slope form, with slope $m$ and the point $(x_1,y_1)$ is :

$\Rightarrow y-y_1=m(x-x_1)$

Here, $x_1=0\mathrm{and}{y}_1=c$ ;

On substituting values,

$$\begin{gathered} \Rightarrow y-c=m(x-0) \\ \Rightarrow y-c=mx \\ \Rightarrow \mathbf{}\mathit{y}\mathbf{}\mathbf{=}\mathbf{}\mathit{m}\mathit{x}\mathbf{}\mathbf{+}\mathit{c} \end{gathered}$$

Hence proved.