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3 years ago

What is the gradient of the line 3y=2x-6

Mathematics

1 answer:

Karo-lina-s [1.5K]3 years ago

7 0

Answer:

2/3

Step-by-step explanation:

The gradient of any line in standard form, Ax + By = C is -A/B.

Divide each term by 3 and simplify.

3y = 2x - 6

3y / 3 = y

2x / 3 = 2/3x

6 / 3 = 2

So, y = 2 / 3 x - 2

slope or gradient = 2/3

Explanation:

The first step in finding the slope of a line that is written in standard form is to write the equation in slope-intercept form, y=mx+b. To do this, rearrange the variables. The standard form, Ax + By = C can be rewritten as By = -Ax + C.

Divide by B to simplify

In the equation By = -Ax + C, B needs to be distributed through the equation. To do this, divide both sides by B. The answer is y = (-A/B)x + C/B.

Find the slope

Once the equation of the line is in slope-intercept form and is simplified, then the slope equals the term in front of the x variable. In the standard form from step 2, the slope is -A/B.

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-1.2 29 20 Enter the answer as an exact decimal or simplified fraction

Rudiy27

Answer:

ohh

Step-by-step explanation:

6 0

3 years ago

Can someone please help me I do not understand

Readme [11.4K]

The perimeter of a figure is the distance all the way around the figure.

Area is how many units takes up the figure.

Example of perimeter: (attached)

Example of area: (attached, with squares in square)

In this case, the area depends on the perimeter. Count two sides of the rectangle. (Horizontal, and vertically.) Then write what the perimeter is for that. Multiply the two numbers and that will be your area.

Vertically, it is 11. Horizontally, it is 9. I would like you to try to see what to do next, if not, comment!

I hope this helped!

8 0

2 years ago

Can somebody help me with this?

icang [17]

We are given polynomial: $5x^3+8x^2-7x-6$ .

We need to explain why the binomial (x + 2) IS a factor of this polynomial expression and why the binomial (x + 1) IS NOT a factor of this polynomial expression.

Let us set first factor equal to 0 and solve for x.

x+2=0

x=-2.

Plugging x=-2 in given polynomial, we get

$5(-2)^3+8(-2)^2-7(-2)-6 = 5(-8) +8(4)+14-6$

$= -40 +32+14-6$

$=0$

Because x=-2 gives 0 on plugging in given polynomial, so it's factor of given polynomial expression.

Now, let us check second factor x+1=0

x=-1.

Plugging x=-1 in given polynomial, we get

$5(-1)^3+8(-1)^2-7(-1)-6 = 5(-1) +8(1)+7-6$

=-5+8+7-6.

= -4.

Because x=-1 doesn't gives 0 on plugging in given polynomial, so it's not a factor of given polynomial expression.

7 0

2 years ago

Which of the following expressions are polynomials?

AlekseyPX

Answer:

1,3 and 5

Step-by-step explanation:

1) -2(7x + 1) − 5(3x2 + 3x + 2)

= -14x - 2 - 15x^2 - 15x - 10

= -15x^2 - 29x - 12

2) (5x2 − 10x + 8) − (10x2 + 19x + 20)

= 5x^2 - 10x + 8 - 10x^2 - 19x - 20

= -5x^2 -29x - 12

3) (-7x2 − 21x + 13) − (8x2 + 8x + 25)

= -7x^2 - 21x + 13 - 8x^2 - 8x - 25

= -15x^2 - 29x - 12

4) (-19x2 − 4x - 7) + (4x2 + 25x − 5)

= -15x^2 + 21x - 12

5) (-17x2 + 2x − 3) + (2x2 − 31x − 9)

= -15x^2 -29x - 12

6) -2(4x − 15) − 3(5x2 + 7x + 6)

= -8x + 30 - 15x^2 - 21x - 18

= -15x^2 - 29x + 12

5 0

3 years ago

Here’s a graph of a linear function. Write the equation that describes that function. Express it in slope intercept form.

worty [1.4K]

<h3>Answer: y = (1/2)x+3</h3>

slope = 1/2, y intercept = 3

==============================================================

Work Shown:

Pick any two points you want on the line.

I'll pick the two points (0,3) which is the y intercept and also the point (2,4).

------

Find the slope of the line through (x1,y1) = (0,3) and (x2,y2) = (2,4)

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

m = (4 - 3)/(2 - 0)

m = 1/2 is the slope

slope = rise/run = 1/2

rise/run = 1/2 means rise = 1 and run = 2.

This means we go up 1 unit each time we move to the right 2 units.

-----

Since the slope is m = 1/2 and the y intercept is b = 3, we can say

y = mx+b

y = (1/2)x+3

this is the same as y = 0.5x+3 since 1/2 = 0.5

4 0

3 years ago