Question

after 3 days had only four toys made, but after nine days had ten toys made? find point slope and slope intercept.

Answer 1

$\bf \begin{array}{ccll} \stackrel{x}{days}&\stackrel{y}{toys}\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 3&4\\ 9&10 \end{array}\\\\ -------------------------------\\\\ \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ 3 &,& 4~) % (c,d) &&(~ 9 &,& 10~) \end{array}$

$\bf slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{10-4}{9-3}\implies \cfrac{6}{6}\implies 1 \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-4=1(x-3) \\\\\\ y-4=x-3\implies y=x+1$