Question

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)

Answer 1

Writing $5x-2y=-6$ in slope-intercept form:

$5x-2y=-6\\5x+6=2y\\\frac{5x+6}{2}=y\\y=\frac{5}{2}x +3$

The slope of the line is the number before "x", which is $\frac{5}{2}$.

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

So the slope of perpendicular is $-\frac{2}{5}$.

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

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

$y-y_{1}=m(x-x_{1})$

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

$y-(-4)=-\frac{2}{5}(x-5)\\y+4=-\frac{2}{5}x+2\\y+\frac{2}{5}x=2-4\\y+\frac{2}{5}x=-2$

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

$y+\frac{2}{5}x=-2\\5y+2x=-10\\2x+5y=-10$.

THIS IS THE SECOND OPTION.

ANSWER: $2x+5y=-10$