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quester [9]
3 years ago
9

Which of the following give an equation of a line that passes through the point (6/5,-19,5) and is parallel to the line that pas

ses through the organ and point (-2,-12)
A. y= 6x-11
B. y= 6x-19/5
C. y= 6x-6/5
D. y= 6x+1
Mathematics
1 answer:
Ilya [14]3 years ago
6 0
Parallel lines, have the same slope, so the slope of the line through 0,0 and -2,-12, is the same as for the line running through (6/5,-19.5) as well, so what is it anyway?

\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
%   (a,b)
&({{ 0}}\quad ,&{{ 0}})\quad 
%   (c,d)
&({{ -2}}\quad ,&{{ -12}})
\end{array}
\\\\\\
% slope  = m
slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{-12-0}{-2-0}\implies \cfrac{-12}{-2}\implies 6

so, we're looking for the equation of a line whose slope is 6, and goes through (6/5,-19/5)

\bf \begin{array}{lllll}
&x_1&y_1\\
%   (a,b)
&({{ \frac{6}{5}}}\quad ,&{{ -\frac{19}{5}}})
\end{array}
\\\\\\
% slope  = m
slope = {{ m}}= \cfrac{rise}{run} \implies 6
\\\\\\
% point-slope intercept
\stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-\left( -\frac{19}{5} \right)=6\left(x-\frac{6}{5}  \right)
\\\\\\
y+\cfrac{19}{5}=6x-\cfrac{36}{5}\implies y=6x-\cfrac{36}{5}-\cfrac{19}{5}\implies y=6x-\cfrac{55}{5}
\\\\\\
y=6x-11
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