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3 years ago

How do you Graph y-3=1/3(x+1)

Mathematics

1 answer:

jekas [21]3 years ago

6 0

Answer:

You can find the point of intersection of the line with the y-axis and the the point of intersection of the line with the x-axis. See the graph attached.

Step-by-step explanation:

Find the intersection with the y-axis. Substitute $x=0$ into the equation and solve for y:

$y-3=\frac{1}{3}(x+1)\\\\y-3=\frac{1}{3}(0+1)\\\\y-3=\frac{1}{3}(1)\\y=\frac{1}{3}+3\\\\y=\frac{10}{3}$

$y$ ≈3.33

Find the intersection with the x-axis. Substitute $y=0$ into the equation and solve for x:

$y-3=\frac{1}{3}(x+1)$

$0-3=\frac{1}{3}(x+1)\\(-3)(3)=x+1\\-9-1=x\\x=-10$

Now, you know that the line passes through the point (0,3.33) and (-10,0). Now you can graph the function. (Observe the graph attached)

You might be interested in

Ashley started the year with 45 comic books. Each month , she adds 5 more comic books to her collection. Which table correctly r

dybincka [34]

Ashley starts with 45 comics.

So in the first box:
x = 0, y = 45
-------------------------------------------------------------------------------------------------------
Each month, she adds 5 comic books to her collection

x (+1), y (+5) (for each month).

First month.

x = 0
y = 45

Second month

x = 1
y = 45 (+5) = 50

Third month

x = 2
y = 50 (+5) = 55

etc.

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

B) is your best choice, as for every month add (+1), the comic books increase by 5 respectively.

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hope this helps

7 0

3 years ago

Read 2 more answers

Bryson has 14 raspberry scones and 21 strawberry scones. He wants to make as many identical bags of scones as possible . Each ba

Kipish [7]

Answer:

7 bags

Step-by-step explanation:

We solve using Greatest Common Factor Method

We have:

14 raspberry scones and 21 strawberry scones

We find the factors of 14 and 21

The factors of 14 are: 1, 2, 7, 14

The factors of 21 are: 1, 3, 7, 21

Then the greatest common factor is 7.

Therefore, the greatest number of bags Bryson can fill is 7 bags

8 0

3 years ago

You are a lifeguard and spot a drowning child 60 meters along the shore and 40 meters from the shore to the child. You run along

sukhopar [10]

Answer:

The lifeguard should run across the shore a distance of 48.074 m before jumpng into the water in order to minimize the time to reach the child.

Step-by-step explanation:

This is a problem of optimization.

We have to minimize the time it takes for the lifeguard to reach the child.

The time can be calculated by dividing the distance by the speed for each section.

The distance in the shore and in the water depends on when the lifeguard gets in the water. We use the variable x to model this, as seen in the picture attached.

Then, the distance in the shore is d_b=x and the distance swimming can be calculated using the Pithagorean theorem:

$d_s^2=(60-x)^2+40^2=60^2-120x+x^2+40^2=x^2-120x+5200\\\\d_s=\sqrt{x^2-120x+5200}$

Then, the time (speed divided by distance) is:

$t=d_b/v_b+d_s/v_s\\\\t=x/4+\sqrt{x^2-120x+5200}/1.1$

To optimize this function we have to derive and equal to zero:

$\dfrac{dt}{dx}=\dfrac{1}{4}+\dfrac{1}{1.1}(\dfrac{1}{2})\dfrac{2x-120}{\sqrt{x^2-120x+5200}} \\\\\\\dfrac{dt}{dx}=\dfrac{1}{4} +\dfrac{1}{1.1} \dfrac{x-60}{\sqrt{x^2-120x+5200}} =0\\\\\\ \dfrac{x-60}{\sqrt{x^2-120x+5200}} =\dfrac{1.1}{4}=\dfrac{2}{7}\\\\\\ x-60=\dfrac{2}{7}\sqrt{x^2-120x+5200}\\\\\\(x-60)^2=\dfrac{2^2}{7^2}(x^2-120x+5200)\\\\\\(x-60)^2=\dfrac{4}{49}[(x-60)^2+40^2]\\\\\\(1-4/49)(x-60)^2=4*40^2/49=6400/49\\\\(45/49)(x-60)^2=6400/49\\\\45(x-60)^2=6400\\\\$

$x$

As $d_b=x$ , the lifeguard should run across the shore a distance of 48.074 m before jumpng into the water in order to minimize the time to reach the child.