Question

Write the equation of the line that passes through (1, 5) and (–2, 14) in slope-intercept form.

Answer 1

\(\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({\color{red}{ 1}}\quad ,&{\color{blue}{ 5}})\quad
% (c,d)
&({\color{red}{ -2}}\quad ,&{\color{blue}{ 14}})
\end{array}
\\\quad \\
% slope = m
slope = {\color{green}{ m}}= \cfrac{rise}{run} \implies
\cfrac{{\color{blue}{ y_2}}-{\color{blue}{ y_1}}}{{\color{red}{ x_2}}-{\color{red}{ x_1}}}
\\ \quad \\
% point-slope intercept
y-{\color{blue}{ y_1}}={\color{green}{ m}}(x-{\color{red}{ x_1}})\qquad \textit{plug in the values and solve for "y"}\\
\qquad \uparrow\\
\textit{point-slope form}\)

Answer 2

find the slope
use either point's coordinate values
plug them in the point-slope intercept
solve for "y"

be happy
eat ice-cream

Answer 3

okay, so y-5=3(x-1) ??

Answer 4

what did you get for the slope anyway?

Answer 5

\[\frac{ 14-5 }{ -2-1 }\]
so that simplifies to
\[\frac{ 9 }{ -3 }\]
so the slope is -3

Answer 6

yeap that's correct, tis -3 :)

so y -5 = \(\bf -3\) (x-1)
then solving for "y"

y = -3x+3+5
y = -3x+8

Answer 7

o so thats the slope intercept form?

Answer 8

y = -3x + 8
^ ^
slope y-intercept

slope = -3
y-intercept = +8

thus, is called the slope-intercept form :)

Answer 9

so what about point-slope form?

Answer 10

ill make another question so you can get metals ;p

Answer 11

the point slope form is right above :)

\(\bf y-{\color{blue}{ y_1}}={\color{green}{ m}}(x-{\color{red}{ x_1}})\qquad \textit{}\\
\qquad \uparrow\\
\textit{point-slope form}\)