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Ket [755]
2 years ago
12

Algebra: Explain in words how to write an equation that is part one: parallel and then also part two: perpendicular to the equat

ion y=2/3x-4 passing through the point (-2,-5). Write the answer in standard form.
Mathematics
1 answer:
sweet-ann [11.9K]2 years ago
8 0
A line that is parallel has the same slop where a line that is perpendicular has a slop that is negative and reciprocal.

so for the parallel one you don't need to worry about the slop because it will be 2/3x. But yous the point slope equation form

y-y1=m(x-x1)

y+5=2/3(x+2)

y+5=2/3x+ 4/3

y=2/3x-11/3

-2/3x+y=-11/3

multiple by -1 so A inst negative

2/3-y=11/3

For a line that is perpendicular you just need to flip the original 2/3x slope and make it negative.

y+5=-3/2(x+2)

y+5=-3/2x-3

y=-3/2x-8

3/2x+y=-8
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The equation of a line is y=-2x+1. What is the equation of the line that is parallel to the first line and passes through (2,2)?
Murrr4er [49]

Answer:

The equation in slope-intercept form is y=-2x+6.

The equation in standard form is 2x+y=6.

The equation in point-slope form is y-2=-2(x-2).

Step-by-step explanation:

The slope-intercept form of a line is y=mx+b where m is the slope and b is the y-intercept.

Parallel lines will have the same slope and different y-intercept.

Anyways the slope of y=-2x+1 is -2.

So the equation of our line we are looking for is -2.

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

We must inf b using y=-2x+b with (x,y)=(2,2).

y=-2x  +b  with (x,y)=(2,2)

2=-2(2)+b

2=-4+b

Add 4 on both sides:

2+4=b

Simplify:

6=b

The equation is y=-2x+6.

Now it didn't say what form it wanted.

There are some forms I can give you like standard and point-slope form.

There is also general form but it is not too much different from standard form.

Standard form is ax+by=c where a,b, and c are integers if possible.

Point-slope form is y-y1=m(x-x1) where (x1,y1) is a point on the line and m is the slope.

So let's go for standard form (ax+by=c) first:

y=-2x+6

add 2x on both sides:

2x+y=6

This is standard form because it is in the form

ax+by=c.

Ok we know point (2,2) is on our line and we also know we have slope,m, is -2.

Point-slope form is

y-y1=m(x-x1)

y-2=-2(x-2)

8 0
3 years ago
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