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Please help!!!!!! 100 points to best answer plus Brainliest!!!

1.)What is the slope of a line that is perpendicular to a line whose equation is 5y=10+2x ?

2.)Line a is represented by the equation y=−2x+3 .
How do these equations compare to line a?
categories: Parallel to line a, Perpendicular to line a, Neither parallel nor perpendicular to line a. Equations: Y=2x-1, Y=-2x+5, Y=1/2x+7.

3.)What is the equation of a line that passes through the point (5, −4) and is parallel to the line whose equation is 2x + 5y = 10?

Respuesta :

Answer:

1.) [tex]-\frac{5}{2}[/tex]

2.) y = 2x - 1 is neither parallel nor perpendicular to line a.

y = - 2x + 5 is parallel to line a.

[tex]y = \frac{1}{2} x + 7[/tex] line is perpendicular to line a.

3.)2x + 5y = -10

Step-by-step explanation:

1.) Given straight line is 5y = 10 + 2x

⇒ [tex]y = \frac{2}{5} x + 2[/tex]

So, the slope of the given line is [tex]\frac{2}{5}[/tex]

Therefore, the slope of the straight line which is perpendicular to the above line will be [tex]-\frac{5}{2}[/tex]

{Since the product of slopes of two perpendicular straight line is -1}

2.) Line a is y = - 2x + 3

Now, y = 2x - 1 is neither parallel nor perpendicular to line a.

y = - 2x + 5 is parallel to line a.

And [tex]y = \frac{1}{2} x + 7[/tex] line is perpendicular to line a.

3.) The equation of the straight line which is parallel to line 2x + 5y = 10 will be 2x + 5y = c, where c is any constant.

If this parallel line passes through (5,-4), then c = 2(5) + 5(- 4) = -10

So the equation of the parallel line is 2x + 5y = -10 (Answer)

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