Question

Write the equation of the line given the following information through (2,4) and (3,7)

Answer 1

`\bf (\stackrel{x_1}{2}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{7}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{7-4}{3-2}\implies \cfrac{3}{1}\implies 3 \\\\\\ \begin{array}c \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-4=3(x-2) \\\\\\ y-4=3x-6\implies y=3x-2`

Answer 2

(2,4) and (3,7)
y=mx+b

4=(m)(2)+b or 7=(m)(3)+b
b=4-2m or b=7-3m
Set them equal:
4-2m=7-3m
m=3

b=4-2m
b=4-2(3)
b=4-6
b=-2

y=mx+b
y=3x-2