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OleMash [197]
3 years ago
13

What is the equation of the line that contains the points (0, 5) and (3, 7)?

Mathematics
1 answer:
ale4655 [162]3 years ago
4 0

To find an equation of a line, you have to know the value of slope first. We can find the value of slope by using the formula below:

\large \boxed{m =  \frac{y_2 - y_1}{x_2 - x_1} }

m-term represents the slope from y = mx+b.

We are given two coordinate points. Substitute the points in the formula.

\large{m =  \frac{7 - 5}{3 - 0} } \\  \large{m =  \frac{2}{3} }

Therefore the slope is 2/3.

Next we find the y-intercept. In the form of y = mx+b where m = slope and b = y-intercept. We have got slope, except the y-intercept. We can find the y-intercept by substituting one of gjven points in the equation of y = mx+b.

Since we know the slope - we can rewrite the equation like below:

\large{y =  \frac{2}{3} x + b}

Then choose one of two points to substitute. I will choose (0,5). Therefore substitute x = 0 and y = 5.

\large{5 =  \frac{2}{3} (0) + b} \\  \large{5 = 0 + b} \\  \large{b = 5}

Thus the y-intercept is (0,5). Note that if the question gives you (0,a) point. That is the y-intercept of graph. So b = a if given (0,a).

Rewrite the equation by substituting the b-value.

\large{y =  \frac{2}{3} x + 5}

Hence, the equation of a line that contains those points is y = 2x/3 + 5

Answer

  • y = 2x/3 + 5

Hope this helps! Let me know if you have any doubts.

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A 0.143-Henry Inductor is connected in series with a variable resistor to a 208-volt 400-cycle source. For what value of capacit
aleksandr82 [10.1K]

Answer:

A.)359.2, B.)2.5 uf

Step-by-step explanation:

E / I = R

208 / 1.04 = 200 ohms

2*pi*f*L = Xl

6.28*400*.143 = 359.2 ohm

1 / (2*pi*f*Xc) = c

1 /(6.28*400*159.2) = 2.5 uf

8 0
3 years ago
(-4)-(-2)-{(-5)-[(-7)+(-3)-(-8)]}
olasank [31]

Answer:

1

Explanation:

I used the calculator.

4 0
3 years ago
Identify the transformation that was applied to this letter.
Shtirlitz [24]
Identify the transformation that was applied to this letter.

D. Rotation about the origin
8 0
2 years ago
Each cone of the hourglass has a height of 12 millimeters. The total height of the sand within the top portion of the hourglass
Harman [31]

The solution would be like this for this specific problem:

Volume of a cylinder = pi * r^2 * h 

Volume of a cone = 1/3 * pi * r^2 * h 

Total Height = 47

Height of the cone = 12

Height of the cylinder = 35

If the top half is filled with sand, then:

volume (sand) = pi * 4^2 * 36

volume (cone) =  1/3 * pi * 4^2 * 12

Total volume = 1960.353816 cubic millimeters

353816 / (10 * pi) = 62.4 seconds.

It will take 62.4 seconds until all of the sand has dripped to the bottom of the hourglass.

7 0
3 years ago
Which of the following is the solution for 7 - 4x ≥ 35 ?
melamori03 [73]
There are no solutuons listed (says which of the following). My answer below should be in the list to choose from.

7 - 4x ≥ 35
subtract 7 from both sides

-4x ≥ 28
divide both sides by -4 AND change the direction of the inequality sign because we're dividing by a negative

x ≤ -7

CHECK:
7 - 4x ≥ 35
7 - 4(-7) ≥ 35
7 + 28 ≥ 35
35 ≥ 35

ANSWER: x ≤ -7

Hope this helps! :)
7 0
3 years ago
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