Question

Indicate in standard form the equation of the line passing through the given points.

G(4, 6), H(1, 5)

Answer 1

\(\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
G&({\color{red}{ 4}}\quad ,&{\color{blue}{ 6}})\quad
% (c,d)
H&({\color{red}{ 1}}\quad ,&{\color{blue}{ 5}})
\end{array}
\\\quad \\
% slope = m
slope = {\color{green}{ m}}= \cfrac{rise}{run} \implies
\cfrac{{\color{blue}{ y_2}}-{\color{blue}{ y_1}}}{{\color{red}{ x_2}}-{\color{red}{ x_1}}}
\\ \quad \\
% point-slope intercept
y-{\color{blue}{ y_1}}={\color{green}{ m}}(x-{\color{red}{ x_1}})\qquad \textit{plug in the values and move everything to the left}\\
\qquad \uparrow\\
\textit{point-slope form}\)

Answer 2

first we find the slope by using the slope formula
slope(m) = (y2 - y1) / (x2 - x1)
(4,6)...x1 = 4 and y1 = 6
(1,5)...x2 = 1 and y2 = 5
now we sub
slope(m) = (5 - 6) / (1 - 4)
can you finish and find the slope ?

Answer 3

-1/-3?

Answer 4

yeap, the slope is\(\bf \cfrac{-1}{-3}\implies \cfrac{1}{3}\) thus

now plug in the \(x_1 \ and \ y_1\) values in the point-slope form


\(\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
G&({\color{red}{ 4}}\quad ,&{\color{blue}{ 6}})\quad
% (c,d)
H&({\color{red}{ 1}}\quad ,&{\color{blue}{ 5}})
\end{array}
\\\quad \\
% slope = m
slope = {\color{green}{ m}}= \cfrac{1}{3}

\\ \quad \\
% point-slope intercept
y-{\color{blue}{ 6}}={\color{green}{ \cfrac{1}{3}}}(x-{\color{red}{ 4}})\qquad \textit{plug in the values and move everything to the left}\\
\qquad \uparrow\\
\textit{point-slope form}\)

so, when you move everything to the left-side, the only thing left on the right-side will be a zero =0