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nikdorinn [45]
3 years ago
8

Find the slope of the line 3x – 2y = 6 (hint: find 2 points; then use the slope formula)

Mathematics
1 answer:
Keith_Richards [23]3 years ago
8 0
3x - 2y = 6

Your hint gives you a longer method of find the slope for the line. When we are given the equation of the line, we shouldn't bother to find two points. It's only when we are given a graph that using two points to find the slope is helpful.

To find the slope of 3x - 2y = 6, we first need to convert it into slope-intercept form.

Slope-intercept form is y = mx + b. Where m is the slope and b is the y-intercept.

If we solve for y in the equation they gave you, we have converted it into slope-intercept form and it will be easy to find the slope.

3x - 2y = 6

Add 2y on both sides.

3x = 6 + 2y

Subtract 6 on both sides.

3x - 6 = 2y

2y = 3x - 6

Divide by 2 on both sides.

y = (3/2)x - 3

This is now in the form of y = mx + b

y = (3/2)x - 3
y = mx + b

You can see that m = 3/2 and that b = -3

That means that the slope is 3/2 and that the y-intercept is -3.

The slope of the line 3x - 2y = 6 is 3/2 OR 1.5 OR 1 1/2.
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katie is planting a garden for her science fair project. she needs 2/3 of a cup of soil to go in 8 different pots.how many cups
Brilliant_brown [7]

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5 and 1/3 cups of soil

Step-by-step explanation:

Hello there, in this problem we can solve for the amount of soil that Katie will need by multiplying the factor for one of them by the number of pots we have, 8. We get 16/3 cups of soil, or 5 and 1/3 cups of soil.

Hope this helps!

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I don't understand how to do find x and y, please help? thank yous.
pav-90 [236]

#8) There are THREE right-angle (90°) TRIANGLES.

The "big" triangle has legs "x" and "no designation - <em>so lets call it Z" </em>and hypotenuse "4+5"<em> = 9</em>

The "left" triangle has legs "4" and "y" and hypotenuse "x"

The "right" triangle has legs "5" and "y" and hypotenuse "no designation - <em>which we named Z</em>"

Now, you can create a system of equations - you have three unknown variables and can create an equation for each triangle using the Pythagorean Theorem.

Big: x² + Z² = 9² → x² + Z² = 81

Left: 4² + y² = x² → 16 + y² = x² → 16 = x² - y² → x² - y² = 16

Right: 5² + y² = Z² → 25 + y² = Z²

Next, let's eliminate Z by using substitution....use the Right equation to plug Z² into the Big equation to create a NEW Big equation.

NEW Big: x² + (25 + y² ) = 81 → x² + y² = 81 - 25 → x² + y² = 56

Now, we have two unknown variables (x and y) and two equations (NEW Big and Left). Solve the system using any method. <em>I am going to solve using the elimination method)</em>

NEW Big: x² + y² = 56

+ Left: <u>x² - y² = 16</u>

2x² = 72 <em>added the NEW Big and Left equations</em>

x² = 36 <em>divided both sides by 2</em>

x = 6 <em>took square root of both sides (NOTE: -6 is disregarded because we are solving for a length, which cannot be negative) </em>

The last step is to plug the "x" value (<em>that we just solved for)</em> into one of the equations to solve for "y". <em>I am choosing to use the Left equation.</em>

<em> </em>x² - y² = 16

36 - y² = 16<em> </em>

- y² = 16 - 36

- y² = -20

y² = 20

y = √20

y = 2√5

Answer: x = 6, y = 2√5

Try #9 on your own and then check your answers below:

Big: Z² + x² = 12², Left: 3² + y² = Z², Right: y² + 9² = x²

Answer: x = 6√3, y = 3√3

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