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Georgia [21]
3 years ago
6

Find the sum of the given polynomials. 5m + 2n, n - 3m, and 7 - 3n

Mathematics
1 answer:
Nataly_w [17]3 years ago
7 0
5m+2n+n-3m+7-3n =2m +7
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What is the equation of the line?
spin [16.1K]

Answer:

y=1/2x+2

Step-by-step explanation:

You want to find the equation for a line that passes through the two points:

(0,2) and (-4,0).

First of all, remember what the equation of a line is:

y = mx+b

Where:

m is the slope, and

b is the y-intercept

First, let's find what m is, the slope of the line...

The slope of a line is a measure of how fast the line "goes up" or "goes down". A large slope means the line goes up or down really fast (a very steep line). Small slopes means the line isn't very steep. A slope of zero means the line has no steepness at all; it is perfectly horizontal.

For lines like these, the slope is always defined as "the change in y over the change in x" or, in equation form:

So what we need now are the two points you gave that the line passes through. Let's call the first point you gave, (0,2), point #1, so the x and y numbers given will be called x1 and y1. Or, x1=0 and y1=2.

Also, let's call the second point you gave, (-4,0), point #2, so the x and y numbers here will be called x2 and y2. Or, x2=-4 and y2=0.

Now, just plug the numbers into the formula for m above, like this:

m= 0 - 2-4 - 0 or... m= -2-4 or... m=1/2

So, we have the first piece to finding the equation of this line, and we can fill it into y=mx+b like this:

y=1/2x+b

Now, what about b, the y-intercept?

To find b, think about what your (x,y) points mean:

(0,2). When x of the line is 0, y of the line must be 2.

(-4,0). When x of the line is -4, y of the line must be 0.

Because you said the line passes through each one of these two points, right?

Now, look at our line's equation so far: y=1/2x+b. b is what we want, the 1/2 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the two points (0,2) and (-4,0).

So, why not plug in for x and y from one of our (x,y) points that we know the line passes through? This will allow us to solve for b for the particular line that passes through the two points you gave!.

You can use either (x,y) point you want..the answer will be the same:

(0,2). y=mx+b or 2=1/2 × 0+b, or solving for b: b=2-(1/2)(0). b=2.

(-4,0). y=mx+b or 0=1/2 × -4+b, or solving for b: b=0-(1/2)(-4). b=2.

See! In both cases we got the same value for b. And this completes our problem.

The equation of the line that passes through the points

(0,2) and (-4,0)

is

y=1/2x+2

4 0
3 years ago
Find the solution to the system of equations below
djverab [1.8K]

Answer:

(4,7)

Step-by-step explanation:

7 0
2 years ago
Identify the vertex of the function graphed below.
saw5 [17]
(3,-2) is the vertex
7 0
2 years ago
Could someone please explain this problem to me?
disa [49]

Answer:

8/3

Step-by-step explanation:

Because all 4 angles are congruent, the sides are proportional.

the scale factor is 5/30 = 1/6.

meaning x = 16(1/6)=8/3.

7 0
2 years ago
Y = (3x)2 + 17 <br> when x = 2
Andrew [12]

Answer:

y = 29

Step-by-step explanation:

y = (3x)2 + 17

y = (3(2))2 + 17

y = (6)2 + 17

y = 12 + 17

y = 29

8 0
2 years ago
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