Question

Write the equation of the line that passes through (−3, 5) and (2, 10) in slope-intercept form

Answer 1

\(\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({\color{red}{ -3}}\quad ,&{\color{blue}{ 5}})\quad
% (c,d)
&({\color{red}{ 2}}\quad ,&{\color{blue}{ 10}})
\end{array}
\\\quad \\
% slope = m
slope = {\color{green}{ m}}= \cfrac{rise}{run} \implies
\cfrac{{\color{blue}{ 10}}-{\color{blue}{ 5}}}{{\color{red}{ 2}}-{\color{red}{ (-3)}}}\implies \cfrac{5}{2+3}\implies \cfrac{\cancel{5}}{\cancel{5}}\implies 1
\\ \quad \\
% point-slope intercept
y-{\color{blue}{ 5}}={\color{green}{ 1}}(x-{\color{red}{ (-3)}})\qquad \textit{plug in the values and solve for "y"}\\
\qquad \uparrow\\
\textit{point-slope form}\)

Answer 2

y-5=x+3

Answer 3

yeap, then solve for "y"
to end up with the slope-intercept form

Answer 4

y=-10

Answer 5

hmm
y-5 +5 = x+3 + 5 <--- adding 5 to both sides
y = x+8