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

[tex]A) \ y = -\frac{2}{5}x-2 \\ \\ B) \ 2x+5y=-10 \therefore y=-\frac{2}{5}x-2 \\ \\ C) \ 2x-5y=-10 \therefore y=\frac{2}{5}x+2 \\ \\ D) \ y+4=-\frac{2}{5}(x-5) \therefore y=-\frac{2}{5}x-2 \\ \\ E) \ y-4=\frac{5}{2}(x + 5) \therefore y=\frac{5}{2}x+\frac{33}{2}[/tex]

For two perpendicular lines it is true that the product of its slopes is:

[tex]m_{1}m_{2}=-1[/tex]

[tex]m_{1}m_{2}=-1 \\ \\ m_{1} \ is \ the \ slope \ of \ y=\frac{5}{2}x+3, \ that \ is, \ m_{1}=\frac{5}{2} \\ \\ Then, \ the \ slope \ of \ a \ perpendicular \ line \ is: \\ \\ m_{2}=-\frac{2}{5}[/tex]

According to this, only A) B) and D) might be the perpendicular lines we are looking for. Notice that these lines are the same. The other condition is that the line must pass through the point (5, -4). By substituting this point in the equation, we have:

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

Finally, the right answer are:

[tex]A) \ y = -\frac{2}{5}x-2 \\ \\ B) \ 2x+5y=-10 \\ \\ D) \ y+4=-\frac{2}{5}(x-5)[/tex]

psm22415 psm22415 · Answer 2 · 2022-02-08T07:10:41+01:00

The equations represent the line that is perpendicular to the line 5x − 2y = −6 and pass through the point (5, −4) is 2x + 5y = −10''.

The correct option is B.

We have to determine

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

What is the general equation of a line?

The standard equation of the line is;

[tex]\rm y=mx+c[/tex]

Where m is the slope of the line.

The given equation of a line is;

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

On comparing with the standard equation of line the slope of the line is 5/2.

When two lines are perpendicular then the line which is perpendicular to the other is equal to;

[tex]\rm m_1\times m_2=-1\\\\\dfrac{5}{2} \times m_2=-1\\\\m_2=\dfrac{-2}{5}[/tex]

Therefore,

The equations represent the line that is perpendicular to the line 5x − 2y = −6 and pass through the point (5, −4) is;

[tex]\rm y-(-4)=\dfrac{-2}{5}(x-5)\\\\5(y+4) = -2x+10\\\\5y+20=-2x+10\\\\5y+2x=-10[/tex]

Hence, The equations represent the line that is perpendicular to the line 5x − 2y = −6 and pass through the point (5, −4) is 2x + 5y = −10.

To know more about the Equation of line click the link given below.

https://brainly.com/question/9889720