What is the slope of the line? * 3 2 6 5 other: ______

Find the equation of a line passing through points (-7, -10) , (-5, -20)

LuckyWell [14K]

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

(-7,-10) and (-5,-20).

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

y = mx+b

here, m is the slope, 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.

Consider (-7,-10) as point #1, so the x and y numbers given will be called x1 and y1. Or, x1=-7 and y1=-10.

Consider (-5,-20), point #2, so the x and y numbers here will be called x2 and y2. Or, x2=-5 and y2=-20.

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

m= (-20 - -10)/(-5 - -7)

m= -10/2

m=-5

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=-5x+b

Now, what about b, the y-intercept?

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

(-7,-10). When x of the line is -7, y of the line must be -10.

(-5,-20). When x of the line is -5, y of the line must be -20.

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

Now, look at our line's equation so far: y=-5x+b. b is what we want, the -5 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 specifically passes through the two points (-7,-10) and (-5,-20).

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:

(-7,-10). y=mx+b or -10=-5 × -7+b, or solving for b: b=-10-(-5)(-7). b=-45.

(-5,-20). y=mx+b or -20=-5 × -5+b, or solving for b: b=-20-(-5)(-5). b=-45.

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 (-7,-10) and (-5,-20) is y=-5x-45.

8 0

3 years ago

What’s the answer to #12? and why

Elena L [17]

Remark
If there are 5 distinct zeros that means either that the x axis is crossed the x axis 5 different places or touched the x axis in 1 place out the 5. Touching in one place means that an even number of roots are the same.

So let's go through all of them to get an answer of 5.

A has 4 x intercepts. It is not the right answer. We need 5.
B has 4 x intercepts. It is not the right answer. We need 5.
C has 6 x intercepts. Not the one we want.
D has 5 x distinct zeros. The wording is a bit tricky. It does not matter than one of them just touches the x axis. There could be an even number of distinct zeros there, but it only counts as one root.

An example of such a graph is f(x)= $\left(\frac{1}{10}(x+2)(x+1.5)(x+1)(x-2)^4(x-3)\right)$

Answer D <<<<<

6 0

3 years ago

Read 2 more answers

If F(x) = 2 - xand w(x) = x - 2, what is the range of (w•p(x)?

hoa [83]

Answer:

Th Range is [0, -∞)

Step-by-step explanation:

f(x) = 2 - x

w(x) = x - 2

We want to find the range of (f * w)(x).

First, we need to find (f * w)(x), which is the multiplication of the function f(x) and the function w(x). Lets use algebra to find (f * w)(x):

$(f*w)(x)=(2-x)(x-2)\\=2x-4-x^2+2x\\=-x^2+4x-4$

This is a quadratic function (U shaped), or a parabola. The graph is attached.

The range is the set of y-values for which the function is defined.

We see from the graph that the parabola is upside down and the highest value is y = 0 and lowest goes towards negative infinity. So the range is from 0 to negative infinity. Or,

0 < y < ∞

In interval notation, that would be:

[0, -∞)

4 0

3 years ago

Which equations represent functions?

never [62]

Answer:

2x + 3y = 10, 3y = 18 (in both cases, for each input x, there is exactly one output y.

Step-by-step explanation:

3y = 10 - 2x, or y = (1/3)(10 - 2x) Yes, this is a function.

4x = 16 → x = 4 NOT a Function, because for x = 4 there are an infinite number of possible y -values

2x - 3 = 14 → 2x = 17 → x = 17/2 Not a function. See reason given above.

3y = 18 → y = 6 Function

2x = 14.6 → x = 7.3 Not a function. See reason given above

4 0

3 years ago

. A survey of 30 students is taken. 11 students say that mathematics is their favorite subject. Based on this survey, how many s

Sveta_85 [38]

Ok, so based on a survey - you know that out of 30 students, 11 said that their favourite subject is mathematics. :-)

This means that:

11/30 of these students think mathematics if their favourite subject.

Now, in order to answer your question, we are going to have to change the denominator of the fraction above to 1000. Whatever we do to the denominator of this fraction, we must do to the numerator of this fraction.

Example:

$\frac { 11 }{ 30 } \times \frac { \frac { 1000 }{ 30 } }{ \frac { 1000 }{ 30 } } \\ \\ =\frac { \frac { 11000 }{ 30 } }{ 1000 } \\ \\ =\frac { 366.\dot { 6 } }{ 1000 }$

This means that rounded to the nearest ten, theoretically speaking, 370 students out of 1000 would say that mathematics is their favourite subject.

7 0

3 years ago

Read 2 more answers

What is the slope of the line? * 3 2 6 5 other: _______