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2 years ago

What is the equation of the line that is parallel to the line y =1/3 x + 4 and passes through the point (6, 5)?

Mathematics

1 answer:

lianna [129]2 years ago

5 0

Answer:

y = $\frac{1}{3}$ x + 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = $\frac{1}{3}$ x + 4 ← is in slope- intercept form

with slope m = $\frac{1}{3}$

Parallel lines have equal slopes , then

y = $\frac{1}{3}$ x + c ← is the partial equation

To find c substitute (6, 5) into the partial equation

5 = 2 + c ⇒ c = 5 - 2 = 3

y = $\frac{1}{3}$ x + 3 ← equation of parallel line

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Estelle is raking leaves in her yard. After 1 hour, she has 2 bags of leaves. After 3 hours, she has 6 bags of leaves. Which gra

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2 years ago

Find the equation of a line that passes the points (5, -9) and (0, -3)

kobusy [5.1K]

Answer:

y = -6/5x - 3

Step-by-step explanation:

Point Slope Form: (y - y1) = m(x - x1)

<u>Step 1: Find Slope</u>

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

m = $\frac{-3 - (-9)}{0 - 5}$

m = $\frac{-3 + 9}{-5}$

m = $\frac{6}{-5}$

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Answer: y = -6/5x - 3

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2 years ago

Read 2 more answers

a share of stock in the bree medical supply company is quoted at 35 1/4. suppose you hold 20 shares of that stock, which you bou

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Total number of stocks bought = 20
Rate at which each stocks were bought = 31 1/2
   = 63/2
Rate at which 20 stocks were bought = 20 * (63/2) dollars
   = 10 * 63 dollars
   = 630 dollars
Rate at which each stocks were sold = 35 1/4
   = 141/4 dollars
Rate at which 20 stocks were sold = 20 * (141/4) dollars
   = 5 * 141 dollars
   = 705 dollars
Then
Amount of profit made by selling 20 stocks = (705 - 630) dollars
      = 75 dollars
So the total amount of profit made is $75. The correct option in regards to the given question is option "D".

3 0

2 years ago

Please help

user100 [1]

Answer:

Length of garden will be 30 metres.

Step-by-step explanation:

Let the Width of garden be x metres.

then,

Length of garden will be (x+6) metres.

Area = Length × Breadth

720 = x X (c+6)

720 = x²+6x

0 = x²+6x-720

As we can see above equation is a quadratic equation in the form of ax²+bx+C.

so,

$= \frac{ - b ± \sqrt{{b}^{2} - 4ac} }{2a} \\ = \frac{ - 6 ± \sqrt{{6}^{2} - 4 \times 1 \times - 720} }{2} \\ = \frac{ - 6 ± \sqrt{36 + 2880} }{2} \\ = \frac{ - 6 ± \sqrt{2916} }{2} \\ = \frac{ - 6 ± 54}{2}\\= \frac{-6+54}{2} ... \frac{ - 6 - 54}{2} \\ = \frac{48}{2} ... \frac{ - 60}{2} \\ = 24... - 30$

One of the Roots of the Quadratic equation is 24 and other is -30.

And as we know width of any garden cannot be negative so the width of garden will be 24 metres.

As we got the width,

adding 6 to it will give us the Length,

So,

24 metres + 6 = 30 metres.

Length of the garden is 30 metres.

Hope It Helped You ;)

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8 0

2 years ago