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2 years ago

Find an equation for the line that passes through the points (-4.-2) and (5,1)

Mathematics

1 answer:

skelet666 [1.2K]2 years ago

6 0

Answer:

y= $\frac{1}{3}$ x- $\frac{2}{3}$

Step-by-step explanation:

The first step to making an equation of a line is finding the slope. To do this, we can use the point slope formula: $\frac{y_2-y_1}{x_2-x_1}$

In this case,

y2=1

y1= -2

x2=5

x1= -4

plug this into the formula: $\frac{1-(-2)}{5-(-4)}$ , which gives us 3/9, or 1/3 as the slope.

Now we have the equation y=1/3x+b. Let's find b! We can do this by plugging in one of the points into our new equation, let's use (5,1)

1=y, 5=x

1= $\frac{1}{3}$ (5)+b

b= - $\frac{2}{3}$

now, we plug b= -2/3 into our equation, and we finally get y= $\frac{1}{3}$ x- $\frac{2}{3}$

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Plssss help 30 pointsss<br><br> If your slope is 1/3 how do you move horizontally?

sweet [91]

What is 1/3 as a slope?

The answer is approximately 18.43º. A slope of 1 in 3 means the slope is 1/3. It also means a rise of 1 and a run of 3. On a graph, starting at the origin, go up 1 unit, then from there, go to the right 3 units.

(hope this helps) :)

7 0

3 years ago

Use matrices and elementary row to solve the following system:

LiRa [457]

I assume the first equation is supposed to be

$5x-3y+2z=13$

and not

$5x-3x+2x=4x=13$

As an augmented matrix, this system is given by

$\left[\begin{array}{ccc|c}5&-3&2&13\\2&-1&-3&1\\4&-2&4&12\end{array}\right]$

Multiply through row 3 by 1/2:

$\left[\begin{array}{ccc|c}5&-3&2&13\\2&-1&-3&1\\2&-1&2&6\end{array}\right]$

Add -1(row 2) to row 3:

$\left[\begin{array}{ccc|c}5&-3&2&13\\2&-1&-3&1\\0&0&5&5\end{array}\right]$

Multiply through row 3 by 1/5:

$\left[\begin{array}{ccc|c}5&-3&2&13\\2&-1&-3&1\\0&0&1&1\end{array}\right]$

Add -2(row 3) to row 1, and add 3(row 3) to row 2:

$\left[\begin{array}{ccc|c}5&-3&0&11\\2&-1&0&4\\0&0&1&1\end{array}\right]$

Add -3(row 2) to row 1:

$\left[\begin{array}{ccc|c}-1&0&0&-1\\2&-1&0&4\\0&0&1&1\end{array}\right]$

Multiply through row 1 by -1:

$\left[\begin{array}{ccc|c}1&0&0&1\\2&-1&0&4\\0&0&1&1\end{array}\right]$

Add -2(row 1) to row 2:

$\left[\begin{array}{ccc|c}1&0&0&1\\0&-1&0&2\\0&0&1&1\end{array}\right]$

Multipy through row 2 by -1:

$\left[\begin{array}{ccc|c}1&0&0&1\\0&1&0&-2\\0&0&1&1\end{array}\right]$

The solution to the system is then

$\boxed{x=1,y=-2,z=1}$

5 0

3 years ago

The sum of Jessica and her father is 42. If her father is 5 times her age, find the age of Jessica

Nostrana [21]

Answer:

8 and a half

Step-by-step explanation:

you will divide 42 and the 5

8 0

3 years ago

Read 2 more answers

A container has 360 gallons ; daniel took 1/3 of water to give to the animals in the ranch; how many gallons of water are left?

Mrrafil [7]

Answer: 240 gallons

Step-by-step explanation:

From the question, we are informed that the container has 360 gallons and that Daniel took 1/3 of water to give to the animals in the ranch. Therefore, the amount of water that Daniel took will be:

= 1/3 × 360

= 120 gallons

Since we have 360 gallons at the beginning and Daniel has taken 120 gallons, the amount of gallons that'll be left will be:

= 360 - 120

= 240 gallons

8 0

3 years ago

What degree of rotation about the origin will cause the triangle below to map onto itslef

drek231 [11]

Answer:

$360^o$