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3 years ago

A line passes through (3, -2) and (6,2). Write an equation for the line in point-slope form.

Mathematics

1 answer:

snow_lady [41]3 years ago

7 0

Answer:

4x - 3y -18 = 0 or y = 4x/3 - 6

Step-by-step explanation:

We will have to find the slope of the line first

The formula for slope:

$m =\frac{y_{2}- y_{1} }{x_{2} -x_{1} } \\m= \frac{-2-2}{3-6}\\ =\frac{-4}{-3}\\ =\frac{4}{3}$

The standard form of equation of a line is:

y = mx + b

We know m,

So the equation will be:

$y= \frac{4}{3}x+b$

We have to find the value of b, for that we will put any one of the point in the equation

So, putting (6,2)

2 = 4/3 * 6 + b

2 = 8 +b

b = -6

Putting the value of m and b in the standard form of equation of line,

$y = mx + b\\y = \frac{4}{3}x+(-6)\\y = \frac{4}{3} x - 6\\Multiplying\ both\ sides\ by\ 3\\3y = 4x - 18\\4x - 3y -18 = 0$ ..

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-2x + y = 0 <br><br> -7x + 3y = 2<br>

dsp73

This is a system of equations.
First, you set everything in terms of y.
Take the first equation and move set everything equal to y
y=0+2x
Since it’s 0, you don’t need to put it, so
y=2x works.
Then, you plug y=2x into the bottom equation, for the y.
-7x +3(2x)=2. You do this because now you have the same variable for both and it can be solved easily.
Then you can simplify.
-7x+3x = 2
Then combine like terms.
-4x = 2
Divide by -4 on each side.
x = -1/2
So, now that you have x, you can plug in your x-value back into the top equation.
-2(-1/2) + y = 0
Combine like terms
1+y=0
Get y by itself
y=-1
There you have it!
You can check by plugging in both values to any of the equations. We will use the top one here.
-2(-1/2) + (-1) =0
+1 + -1 = 0
It works!
So,
X= -1/2
Y= -1
Please rate me Brainliest answer :)

3 0

3 years ago

Read 2 more answers

— 2y – Зу +8 = 8 — 5у – 12

jasenka [17]

Answer:

No Solution.

Step-by-step explanation:

Equality equation:

— 2y – Зу +8 = 8 — 5у – 12 (Given)

-5y + 8 = -4 - 5y (distributive property of equality)

-5y = -12 - 5y (subtraction property of equality)

= -12 (addition property of equality)

when you add 5y on both sides it cancels the 5y out, it's no solution.

<em><u>Ace-The Kid Laroi</u></em>

6 0

3 years ago

Solve 2(b − 3) ≥ 3(3 − b) and describe the graph of the solution. Show all your work.

solong [7]

Answer:

$\large\boxed{b\geq3\to b\in[3,\ \infty)}$

Step-by-step explanation:

$2(b-3)\geq3(3-b)\qquad\text{use the distributive property:}\ a(b+c)=ab+ac\\\\(2)(b)+(2)(-3)\geq(3)(3)+(3)(-b)\\\\2b-6\geq9-3b\qquad\text{add 6 to both sides}\\\\2b-6+6\geq9+6-3b\\\\2b\geq15-3b\qquad\text{add}\ 3b\ \text{to both sides}\\\\2b+3b\geq15-3b+3b\\\\5b\geq15\qquad\text{divide both sides by 5}\\\\\dfrac{5b}{5}\geq\dfrac{15}{5}\\\\b\geq3$

$,\ \geq-\text{line to the right}\\-\text{o}\text{pen circle}\\\leq,\ \geq-\text{closed circle}$

4 0

3 years ago

Please help me on this it’s due

olya-2409 [2.1K]

<h3>Answer: 5 cakes</h3>

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

Explanation:

Let's start off converting the mixed number 12 & 1/4 to an improper fraction.

$a \frac{b}{c} = \frac{a*c+b}{c}\\\\12 \frac{1}{4} = \frac{12*4+1}{4}\\\\12 \frac{1}{4} = \frac{49}{4}\\\\$

Do the same for the other mixed number 2 & 1/3.

$a \frac{b}{c} = \frac{a*c+b}{c}\\\\2 \frac{1}{3} = \frac{2*3+1}{3}\\\\2 \frac{1}{3} = \frac{7}{3}\\\\$

-----------------------

From here, we divide the two fractions. I converted them to improper fractions to make the division process easier.

$\frac{49}{4} \div \frac{7}{3} = \frac{49}{4} \times \frac{3}{7}\\\\\frac{49}{4} \div \frac{7}{3} = \frac{49\times 3}{4\times 7}\\\\\frac{49}{4} \div \frac{7}{3} = \frac{7\times 7\times 3}{4\times 7}\\\\\frac{49}{4} \div \frac{7}{3} = \frac{7\times 3}{4}\\\\\frac{49}{4} \div \frac{7}{3} = \frac{21}{4}\\\\$

The last step is to convert that result to a mixed number.

$\frac{21}{4} = \frac{4*5+1}{4}\\\\\frac{21}{4} = \frac{4*5}{4}+\frac{1}{4}\\\\\frac{21}{4} = 4+\frac{1}{4}\\\\\frac{21}{4} = 5 \frac{1}{4}\\\\$

Note that 21/4 = 5.25 and 1/4 = 0.25 to help check the answer.

-----------------------

Therefore, she can make 5 cakes. The fractional portion 1/4 is ignored since we're only considering whole cakes rather than partial ones.

3 0

3 years ago

A clothing manufacturer makes 1,500 pairs of jeans. They ship their jeans to stores in packages of 36. How many full packages wi

Crazy boy [7]

Answer:

a) How many full packages will be used to ship the jeans?

41 packages

b) How many jeans are left over?

24 Jeans

Step-by-step explanation:

We are told that a manufacturer: made 1500 Jeans and is shipping them in packages of 36.

Hence, the number of packages of 36 he can send out to stores is calculated as:

1500÷ 36

= 41.666666667

In whole number packages = 41 packages

Hence, 41 full packages would be used to ship the jeans.

The number of Jeans left behind is

1500 - (41 × 36)

= 1500 - 1476

= 24 Jeans

4 0

2 years ago