Question
Mathematics
Jack Whalen $\phantom{\rule{1em}{0ex}}09/05/2312:1$quad09//05//2312:1
HW Score: $6.25\mathrm{%},1$6.25%,1 of 16
points
Points: 0 of 1
Write the equation of the line passing through the point $\left(5,-5\right)$(5,-5) with slope $-\frac{4}{5}$-(4)/(5).
The equation of the line is
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The equation of a line in point-slope form is given by:
$y-{y}_{1}=m\left(x-{x}_{1}\right)$y-y_(1)=m(x-x_(1))
where $\left({x}_{1},{y}_{1}\right)$(x_(1),y_(1)) is a point on the line and $m$m is the slope of the line.
Substituting the given values, we have:
$y-\left(-5\right)=-\frac{4}{5}\left(x-5\right)$y-(-5)=-(4)/(5)(x-5)
Simplifying the right-hand side, we get:
$y+5=-\frac{4}{5}x+\frac{4}{5}\left(5\right)$y+5=-(4)/(5)x+(4)/(5)(5)
$y+5=-\frac{4}{5}x+4$y+5=-(4)/(5)x+4
Subtracting 5 from both sides, we have:
$y=-\frac{4}{5}x-1$y=-(4)/(5)x-1
Therefore, the equation of the line passing through the point $\left(5,-5\right)$(5,-5) with slope $-\frac{4}{5}$-(4)/(5) is:
$\overline{)y=-\frac{4}{5}x-1}$y=-(4)/(5)x-1
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