which of the following is the equation of the line that is parallel to y= -2x - 14 and goes through the point (-3, 1)

Question

which of the following is the equation of the line that is parallel to y= -2x - 14 and goes through the point (-3, 1)

Answer 1

Parallel lines have the same slope but different y intercepts so the slope will be -2

The line in slope intercept form will be

y = -2x + b

Now we just plug in the coordinates (-3, 1) from above to solve for b

1 = -2(-3) + b

1 = 6 + b

Subtract 6 from both sides of the equation

1 - 6 = b

-5 = b

So the parallel line is

y = -2x - 5

I hope you find this useful if you have any questions please send me a message.

Answer 2

Solution:

A line that is parallel to y = -2x - 14, is a line that has the same slope m = -2 where m = (y2 - y1) / (x2 - x1)

the line passes through point ( -3,1), and the slope m = -2 = (y - 1) / (x + 3) , cross multiply and you have

-2( x +3) = y-1 , y = -2( x+3) + 1 = -2x - 6 +1 = -2x -5 , or y = -2x - 5

Answer 3

To answer this question, you need to know that parallel lines all have the same slope (just a different y-intercept). So, to find the equation of the line that is parallel to y= -2x - 14, we need to first know what the slope of that line is. Our new line will have the same slope.

The slope of a line in the form y = mx + b is the "m" value (the number in front of the "x". In this case, that's -2.

So the equation of our new line will be y = -2x + b, we just need to find the "b". We use the point that was given (-3, 1) to find the "b". Notice that the point is an (x, y) so x = -3 and y = 1. Plug those values into the equation y = -2x + b as the x and y. That gives you: 1 = -2(-3) + b or 1 = 6 + b or b = -5. We can now plug that b value into our equation y = -2x + b to get:

y = -2x - 5

Since you didn't post the possible choices, I'm unsure if this is the form that the answer is in. Another way to do this problem is using the point-slope form of the line which is:

(y - y₁) = m(x - x₁) where m is the slope and the point (x₁, y₁) is a point that the line goes through.

If you did the problem using this method, you plug the point (-3, 1) in for the point (x₁, y₁) to get:

(y - 1) = -2(x - -3) or y - 1 = -2(x + 3)

If you multiply this out and combine like-terms, you'll see that it's the same as y = -2x - 5