Question

will medal, please help!!!

Write the equation of a line that is perpendicular to y=0.25x−7 and that passes through the point (−6,8)(-6,8)(−6,8

Answer 1

hmmm have you covered "slopes" yet?

Answer 2

yeah but for some reason i cant remember how to do it a all :(

Answer 3

well.. what's the slope of \(\Large y=0.25x−7 \)?

Answer 4

0.25

Answer 5

yeap... 0.25... or 1/4
so, a line that is perpendicular to that one, will have a NEGATIVE RECIPROCAL slope
meaning
\(\bf slope=\cfrac{1}{{\color{blue}{ 4}}}\qquad negative\implies -\cfrac{1}{{\color{blue}{ 4}}}\qquad reciprocal\implies - \cfrac{{\color{blue}{ 4}}}{1}\implies -4\)

so.... now we know, the slope of that perpendicular line, is -4
so, what is the line whose slope is -4 and passes through (-6,8)

well, use the given coordinates and slope in the point-slope form
\(\begin{array}{lllll}
&x_1&y_1\\
% (a,b)
&({\color{red}{ -6}}\quad ,&{\color{blue}{ 8}})\quad

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

Answer 6

you're not asked to put it in slope-intercept form, so, that will suffice, otherwise, you can just solve for "y", to put it in slope-intercept form