Question

m= 4/3 ; (0,5/9)
write equation of line in slope intercept form

Answer 1

\(\bf \begin{array}{lllll}
&x_1&y_1\\
% (a,b)
&({\color{red}{ 0}}\quad ,&{\color{blue}{ \frac{5}{9}}})\quad

\end{array}
\\\quad \\
% slope = m
slope = {\color{green}{ m}}= \cfrac{4}{3}
\\ \quad \\
% point-slope intercept
y-{\color{blue}{ y_1}}={\color{green}{ m}}(x-{\color{red}{ x_1}})\qquad \textit{plug in the values and solve for "y"}\\
\qquad \uparrow\\
\textit{point-slope form}\)

Answer 2

slope intercept form is y = mx + b
slope(m) = 4/3
(0,5/9)....x = 0 and y = 5/9
now we sub and since we already have slope(m) and our points (x,y), we basically need to find the y intercept (b)
y = mx + b
5/9 = 4/3(0) + b
5/9 = b

so our equation in slope intercept form is : y = 4/3x + 5/9