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3 years ago

What is the slope of the line below? If necessary, enter your answer as a

Mathematics

1 answer:

Westkost [7]3 years ago

3 0

9514 1404 393

Answer:

6/5

Step-by-step explanation:

The slope formula is useful for finding the slope.

m = (y2 -y1)/(x2 -x1)

m = (-1 -11)/(-5 -5) = -12/-10

m = 6/5

The slope of the line through the given points is 6/5.

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How do you solve the three forms: Slope Y-intercept form Standard Form Point slope form

Nostrana [21]

Answer:An equation in the slope-intercept form is written as

y=mx+b

Where m is the slope of the line and b is the y-intercept. You can use this equation to write an equation if you know the slope and the y-intercept.

Example

Find the equation of the line

Choose two points that are on the line

Calculate the slope between the two points

m=y2−y1x2−x1=(−1)−33−(−3)=−46=−23

We can find the b-value, the y-intercept, by looking at the graph

picture28

b = 1

We've got a value for m and a value for b. This gives us the linear function

y=−23x+1

In many cases the value of b is not as easily read. In those cases, or if you're uncertain whether the line actually crosses the y-axis in this particular point you can calculate b by solving the equation for b and then substituting x and y with one of your two points.

We can use the example above to illustrate this. We've got the two points (-3, 3) and (3, -1). From these two points we calculated the slope

m=−23

This gives us the equation

y=−23x+b

From this we can solve the equation for b

b=y+23x

And if we put in the values from our first point (-3, 3) we get

b=3+23⋅(−3)=3+(−2)=1

If we put in this value for b in the equation we get

y=−23x+1

which is the same equation as we got when we read the y-intercept from the graph.

To summarize how to write a linear equation using the slope-interception form you

Identify the slope, m. This can be done by calculating the slope between two known points of the line using the slope formula.

Find the y-intercept. This can be done by substituting the slope and the coordinates of a point (x, y) on the line in the slope-intercept formula and then solve for b.

Once you've got both m and b you can just put them in the equation at their respective position.

4 0

3 years ago

Solve the problem below

Sliva [168]

Answer:

T = 60 degrees

Step-by-step explanation:

The dotted line is the height so it is a right angle

We are able to use trig functions since this is a right triangle

cos T = adj side / hyp

cos T = a/b

cos T = 8 sqrt(2) / 16 sqrt(2)

cos T = 1/2

Taking the inverse of each side

cos^-1 ( cosT) = cos^-1 ( 1/2)

T = 60 degrees

3 0

2 years ago

Read 2 more answers

PLEASE HELP

valina [46]

Answer:

Step-by-step explanation:

You have 3 unknowns: a, b, and c. It's our job to find them algebraically. I'm going to start with the point where x = 0 and y = 7. You'll see why in a minute. Filling in the standard form of a quadratic

$y=ax^2+bx+c$ using (0, 7):

$7=a(0)^2+b(0)+c$ gives you that c = 7. We will use that value now when we write the next 2 equations. Now the point (-2, 19):

$19=a(-2)^2+b(-2)+7$ and

$19=4a-2b+7$ so

12 = 4a - 2b

Now for the next point (-1, 12):

$12=a(-1)^2+b(-1)+7$ and

$12=a-b+7$ so

5 = a - b

Now we have a system of equations (the 2 bold font equations) that we will solve by elimination:

12 = 4a - 2b

5 = a - b

Multiply the bottom equation by -4 to get a new system:

12 = 4a - 2b

-20 = -4a + 4b

Add those together to get rid of the a terms and end up with

-8 = 2b so

b = -4

Now we can sub in -4 for b to solve for a. I'm using the second bold type equation to do this:

5 = a - (-4) and

5 = a + 4 so

a = 1 and the equation for the quadratic function is

$y=x^2-4x+7$

7 0

3 years ago

Please help solve, will mark brainliest

Neko [114]

Answer:

1/3

Step-by-step explanation:

5 over 15

divide both by 5 to simplify 1 over 3

3 0

3 years ago

What is the explicit formula for this sequence?<br> -7, -3, 1, 5, ...

alukav5142 [94]

Answer:

Step-by-step explanation:

a1 = - 7

d = 4

an = a1 + (n - 1) * d

an = - 7 + (n - 1) * 4

an = - 7 + 4n - 4

an = -11 + 4n

Try this out. Let n = 3

a3 = -11 + 4*3

a3 = - 11 + 12

a3 = 1 Which is what the series says.

8 0

2 years ago