Question

Derive the expression for slope of a line $y=mx+c$

Answer 1

Here, the distance $c$ is called the $\mathrm{y}-\mathrm{intercept}$ of the given line .

So, the coordinate of a point where the line L meets the$y-axis$ will be $(0,c).$

That means, line L passes through a fixed point$(0,c)$ with slope m.

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

$(y–y_1)=m(x–x_1)$

Here, $(x_1,y_1)=(0,c)$

Substituting these values, we get;

$y–c=m(x–0)$

$y–c=mx$

$y=mx+c$

Therefore, the point (x, y) on the line with slope m and $\mathrm{y}-\mathrm{intercept}\mathrm{c}$ lies on the line if and only if $y=mx+c$