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3 years ago

Which linear equation includes the points (6,0) and (0, – 4)?

Mathematics

1 answer:

Lorico [155]3 years ago

8 0

Answer:

y= (2/3)x - 4

Step-by-step explanation:

To answer this you'll want to use the slope intercept form of a line:

y= mx + b

So to solve essentially you just have to find the values for m and b

- m represents the slope of the line

- b is the y-intercept (the point where the line crosses the y-axis)

You can figure that b = -4 because the line will cross the y-axis when x = 0, and you are given the point on the line (0,-4), where x is equal to 0.

Now to find the slope of the line, since you are given two points on the line you will want to use the slope equation:

slope = $\frac{y1-y2}{x1-x2}$

So you can assign each of the two points a number (1 or 2) where its values are equal to (x1, y1) or (x2, y2). It does not matter which point gets which number.

In this example:

We will assign the point (6,0) to be (x1, y1),

and we will assign the point (0, -4) to be (x2, y2)

So we end up with the following:

m= $\frac{0- (-4)}{6-0}$

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m= $\frac{0+4}{6}$

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m= $\frac{4}{6}$

Simplify the fraction:

m = $\frac{2}{3}$

From there you just substitute in for m and b into the slope intercept equation

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I have a question about polynomial division it is in the picture

Cloud [144]

To answer this question, we have to do the long division process for polynomials. We can do the operation as follows:

To do this division process, we have:

1. Divide the first term of the dividend by the first element of the divisor. They are:

$\frac{-4x^3}{4x^2}=-x$

2. Now, we have to multiply this result by the divisor, and the result will change its sign since we have to subtract that result from the dividend as follows:

$-x\cdot(4x^2_{}-4x-4)=-4x^3+4x^2+4x$

And since we to subtract this result from the dividend, we end up with:

$-(-4x^3+4x^2+4x)=4x^3-4x^2-4x$

3. Then we have the following algebraic addition:

$\frac{\begin{cases}-4x^3+24x^2-15x-15 \\ 4x^3-4x^2-4x\end{cases}}{20x^2-19x-15}$

4. Again, we need to divide the first term of the dividend by the first term of the divisor as follows:

$\frac{20x^2}{4x^2}=5$

5. And we have to multiply 5 by the divisor, and the result will be subtracted from the dividend:

$5\cdot(4x^2-4x-4)=20x^2-20x-20$

Since we have to subtract this from the dividend, we have:

$-(20x^2-20x-20)=-20x^2+20x+20$

6. And we have to add this algebraically to the dividend we got in the previous step:

$\frac{\begin{cases}20x^2-19x-15 \\ -20x^2+20x+20\end{cases}}{x+5}$

And this is the remainder of the division, x + 5.

As we can see from the division process, we got as:

1. The quotient: -x + 5

$q=-x+5$

2. The remainder: x + 5.

$R=x+5$

Since we have that the dividend = divisor * quotient + remainder.

Therefore, the result for this division is:

$-4x^3+24x^2-15x-15=(4x^2-4x-4)\cdot(-x+5)+(x+5)$

4 0

1 year ago

What is the slope of the line through the points (–3, 5) and (4, 5)? undefined 0 2 –2

Kazeer [188]

Finding the slope using two points:

The formula for slope is

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

In this case you have the points (-3, 5) and (4, 5):

$y_{2} =5\\y_{1} =5\\x_{2} =4\\x_{1} =-3$

^^^Plug these numbers into the formula for slope...

$\frac{5-5}{4 - (-3)}$

$\frac{0}{7}$

^^^This is your slope

Hope this helped!

~Just a girl in love with Shawn Mendes

7 0

3 years ago

Read 2 more answers

If a line crosses the y-axis at (0, 1) and has a slope of 4/5 , what is the equation of the line?

lawyer [7]

What does this mean

3 0

3 years ago

PLEASE HELP!! Being timed need help asap.

ivanzaharov [21]

If points D, E, F and G make a rectangle with the given coordinates for each point then the area of the rectangle is 150 sq. units

How to find distance between two points?

Distance between two points is the length of the line segment that connects the two points in a plane.

The formula to find the distance between the two points is usually given by D = √((x₂ – x₁)² + (y₂ – y₁)²)

This formula is used to find the distance between any two points on a coordinate plane or x-y plane.

According to the given question:

The four vertices are D(-1,-3), E(-9, -9), F(-18, 3) and G(-10, 9) check the attachment below.

Distance between two points D = √((x₂ – x₁)² + (y₂ – y₁)²)

Side DE = √((-9 – (-1))² + (-9 – (-3))²) = √100 = 10 units

Side EF = √((-18 – (-9))² + (3 – (-9))²) = √225 = 15 units

Side FG = √((-10 – (-18))² + (9 – 3)²) = √100 = 10 units

Side GD = √((-1 – (-10))² + (-3 – 9)²) = √225 = 15 units

∴ Area of rectangle = l x b = DE . EF

Area = 10 x 15 = 150 sq. units

Hence the area of rectangle with the given coordinates is 150 sq. units

To learn more about distance between two points visit

brainly.com/question/24485622

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6 0

1 year ago

Which expression is equivalent to the following complex fraction?

marta [7]

Answer:

$\dfrac{-4x+7}{2(x-2)}$

Step-by-step explanation:

The first step is to combine the parts of the numerator and denominator into one rational expression each. Those will have the same denominator, so their ratio is the ratio of their numerators.

$\dfrac{\dfrac{3}{x-1}-4}{2-\dfrac{2}{x-1}}=\dfrac{\left(\dfrac{3-4(x-1)}{x-1}\right)}{\left(\dfrac{2(x-1)-2}{x-1}\right)}=\dfrac{3-4(x-1)}{2(x-1)-2}\\\\=\dfrac{3-4x+4}{2x-2-2}=\boxed{\dfrac{-4x+7}{2(x-2)}}$

5 0

3 years ago

Read 2 more answers