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3 years ago

The line parellel to 2x+y=5 and passing through (5,4) has equation

Mathematics

1 answer:

mrs_skeptik [129]3 years ago

4 0

Answer:

y=-2x+14

Step-by-step explanation:

If we are looking for a line parallel to 2x+y=5.

Then we are looking for an equation with the same slope as the equation 2x+y=5.

To obtain the slope of equaiton 2x+y=5 I will put it in slope-intercept form.

Luckily there is only one step which is to subtract 2x on both sides.

y=-2x+5

The slope of this line is -2

The slope of parallel line will also be -2.

So we know our equation is in the form y=-2x+b

To find b we will just use the point (x,y)=(5,4) we know is on the line.

Plug in and solve for b.

4=-2(5)+b

4=-10+b

14=b

So the equation that is parallel to 2x+y=5 and goes through (5,4) is y=-2x+14

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3 years ago

PLS HELP

Colt1911 [192]

Answer:

y = -4x-21

Step-by-step explanation:

Hi there!

We want to write an equation of the line that passes through (-4, -5) and is parallel to y=-4x-1.

Parallel lines have the same slopes. So let's find the slope of y=-4x-1.

The line is written in the form y=mx+b, where m is the slope and b is the y intercept.

As -4 is in the place of where m should be, -4 is the slope of y=-4x-1.

It's also the slope of the line parallel to that line.

Right now, what we know about the line parallel to y=-4x-1 is that the slope of it is 4 and it passes through the point (-4, -5).

We can substitute those values into the formula for point-slope form, which is $y-y_1=m(x-x_1)$ , where m is the slope and $(x_1, y_1)$ is a point.

We can label the values of everything to help us avoid confusion.

m=-4

$x_1=-4\\y_1=-5$

Now substitute those values into the formula. Note: the formula contains SUBTRACTION, and we have NEGATIVE numbers. Hence,

$y--5=-4(x--4)$

Now simplify.

$y+5=-4(x+4)$

On the right side, do the distributive property.

y+5=-4x-16

Subtract 5 from both sides.

Hope this helps!

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3 years ago