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Which equations represent the line that is perpendicular to the line 5x − 2y = −6 and passes through the point (5, −4)? Check all that apply.

y = –x – 2
2x + 5y = −10
2x − 5y = −10
y + 4 = –(x – 5)
y – 4 = (x + 5)

Respuesta :

TaeKwonDoIsDead

Writing [tex]5x-2y=-6[/tex] in slope-intercept form:

[tex]5x-2y=-6\\5x+6=2y\\\frac{5x+6}{2}=y\\y=\frac{5}{2}x +3[/tex]

The slope of the line is the number before "x", which is [tex]\frac{5}{2}[/tex].

The slope of the perpendicular to this line is the negative reciprocal of this.

So the slope of perpendicular is [tex]-\frac{2}{5}[/tex].


To find the equation of the perpendicular line, we need a point. It is given as [tex](5,-4)[/tex] where [tex]x_{1}=5[/tex] and [tex]y_{1}=-4[/tex].

Now we use the point-slope form of a line to figure out the equation:

[tex]y-y_{1}=m(x-x_{1})[/tex]

Plugging in the values of [tex]x_{1}[/tex] and [tex]y_{1}[/tex] and [tex]m=-\frac{2}{5}[/tex], gives us:

[tex]y-(-4)=-\frac{2}{5}(x-5)\\y+4=-\frac{2}{5}x+2\\y+\frac{2}{5}x=2-4\\y+\frac{2}{5}x=-2[/tex]

Multiplying everything by 5 [to get rid of the denominator] and re-arranging gives us:

[tex]y+\frac{2}{5}x=-2\\5y+2x=-10\\2x+5y=-10[/tex].

THIS IS THE SECOND OPTION.


ANSWER: [tex]2x+5y=-10[/tex]