Question

Use the slope-intercept form of the linear equation to write the equation of the line with the given slope and y-intercept. Slope 4; y-intercept (0,-8/9)
Type answer in slope-intercept form

Answer 1

Slope-intercept form:   y = mx + b   [m is the slope, b is the y-intercept or the y value when x = 0 ---> (0, y)]

Since you know:

m = 4

$b=-\frac{8}{9}$        Plug it into the equation

y = mx + b

$y=4x-\frac{8}{9}$

Answer 2

$\bf (\stackrel{x_1}{0}~,~\stackrel{y_1}{-\frac{8}{9}}) ~\hspace{10em} \stackrel{slope}{m}\implies 4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{\left(-\cfrac{8}{9} \right)}=\stackrel{m}{4}(x-\stackrel{x_1}{0}) \\\\\\ y+\cfrac{8}{9}=4x\implies y = 4x-\cfrac{8}{9}$