Question

Find the equation of a line that passes through the point (0,1) and has a gradient of 3.

Leave your answer in the form
y
=
m
x
+
c

Answer 1

the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

`(\stackrel{x_1}{0}~,~\stackrel{y_1}{1})\hspace{10em} \stackrel{slope}{m} ~=~ 3 \\\\\\ \begin{array}ll \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{ 3}(x-\stackrel{x_1}{0}) \\\\\\ y-1=3x\implies {\Large \begin{array}{llll} y=3x+1 \end{array}}`