Question

What is the equation of the line with a slope of 2/3 that goes through the point (4,1) in slope-intercept form?
A) 2/3x+5/3
B) -2/3x -5/3
C) -2/3x +5/3
D) 2/3x -5/3

Answer 1

\(\bf \begin{array}{lllll}
&x_1&y_1\\
% (a,b)
&({\color{red}{ 4}}\quad ,&{\color{blue}{ 1}})\quad

\end{array}
\\\quad \\
% slope = m
slope = {\color{green}{ m}}= \cfrac{2}{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

D)