Question

D. Rearrange the equation to solve for the slope, m. Is this equivalent to the equation for slope given inquestion 4F above? Explain,

Answer 1

If we say

`y-y_1=m(x-x_1)`

then dividing both sides by (x - x_1) gives

`(1)/(x-x_1)*(y-y_1)=m(x-x_1)*(1)/(x-x_1)`

`\therefore m=(y-y_1)/(x-x_1)`

which is our answer!

The above equation correctly gives the slope m because it is in accord with the definition of m as rise / run.

(E).

Let us now expand the RHS of the first equation to get:

`y-y_1=mx-mx_1`

Adding y_1 to both sides gives

`\textcolor{#FF7968}{y=mx-mx_1+y_(1.)}`

Or in a more neat form

`\textcolor{#FF7968}{y=mx+(y_1-mx_1)}\text{\textcolor{#FF7968}{.}}`

(F).

As can be seen from the equation y = mx + b we got in E, the y-intercept b is given by

`\textcolor{#FF7968}{b=y_1-mx_(1.)}`