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3 years ago

What is the slope of a line parallel to the line -10x-5y=25?

Mathematics

1 answer:

irinina [24]3 years ago

8 0

Answer:

The slope for the parallel line to the equation -10x-5y=25 is -2

Step-by-step explanation:

First we need to convert the equation to slope-intercept form to determine the slope.

-10x-5y=25

+10x _10x

-5y=25+10x

/-5 /-5

y= -5 -2x

Remember, -5 is the y-intercept and -2 is the slope for this equation. A parallel line is a line that never intersects with the first line. If the two equations have different slopes, they will eventually intersect. Because of this, our parallel line needs to have the same slope as the initial equation: -10x-5y=25

Since we've determined that the slope for that equation is -2, we can infer that this will be the slope for our parallel line.

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(i hope i explained that well enough, i'm better at explaining it algebraically as opposed to putting it into words lol)

answer (algebraic/steps for solving)

first, plug in 5 for $x$ in the equation $2x+3y=10$ .

$2x+3y=10$ ⇒ $2(5)+3y=10$

then plug in 2 for $y$ .

$2(5)+3y=10$ ⇒ $2(5)+3(2)=10$

now your equation is $2(5)+3(2)=10$ . all that's left to do is to simplify. you can do this in whatever order you'd like, but i'll start with multiplying 2 · 5.

$2(5)+3(2)=10$ ⇒ $10 + 3(2) = 10$

multiply 3 · 2.

$10 + 3(2) = 10$ ⇒ $10 + 6 = 10$

add 10 + 6.

$10 + 6 = 10$ ⇒ $16=10$

16 and 10 are not equal, therefore (5, 2) is not a solution to the equation $2x+3y=10$ . in order for a coordinate pair to be the solution to an equation, both sides of the equation need to end up equal after solving and simplifying.

i hope this helps! have a great rest of your day <3

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What is the slope of a line parallel to the line -10x-5y=25?​

What is the slope of a line parallel to the line -10x-5y=25?