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Anit [1.1K]
3 years ago
11

using the point-slope formula, what is the equation of the line that passes through the points (1, 5) and (0, 0)? a. y = x b. y

= 5x c. y = 5x 10 d. y = 5x – 1
Mathematics
1 answer:
Dmitry_Shevchenko [17]3 years ago
4 0
First we find the slope m as follows:
m=\frac{y-y_{1}}{x-x_{1}}=\frac{5-0}{1-0}=5
So the equation is of the form:
y = 5x + b
When x = 1, y = 5. Therefore b = 0.
So the equation is:
y = 5x



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Which of the following equations has a graph that passes through (3, 3) and has a slope of −2?
Tatiana [17]

Answer:

y - y1 = m(x - x1)

y - -3 = 3(x - 1)

y + 3 = 3x - 3

     y = 3x - 3 - 3

     y = 3x - 6

     y = 3x - 6

Step-by-step explanation:

Thie equation is in slope-intercept form (y = mx + b)

The y-intercept is -6 .... ((0, -6) is one point on the line.

It is given that (1, -3) is also on the line. So to graph, plot those

2 points and connect them with a line.

7 0
3 years ago
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Find and simplify the difference quotient f(x + 1) – f(x) for the following function.
ra1l [238]

In your situation you said that

  • f(x) = mx+b
  • m=0

Putting those together, you'd have f(x) =  b because 0\cdot x+b=b.

To evaluate the difference quotient, first find each piece on it's own:

  • f(x+1) = b because f(x) = b no matter what your x-value is.
  • f(x) = b

So putting those together:

     f(x+1) - f(x) = b-b = 0

Remember that the difference quotient is basically finding the slope of something.  Since you were given that the slope is 0, the difference quotient should work out to match that.

3 0
3 years ago
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A student had 500 milliliters of water in a water bottle. She drank 25% of the water before soccer practice. After practice, she
marta [7]

A student had 500 milliliters of water in a water bottle. She drank 25% of the water before soccer practice. After practice, she drank 1/3 of the remaining water.

​How much water, in milliliters, does the student have left in the bottle?

Answer:

the amount of water the student have left in the bottle is 250 milliliters

Step-by-step explanation:

A student had 500 milliliters of water in a water bottle. She drank 25% of the water before soccer practice. After practice, she drank 1/3 of the remaining water.

​How much water, in milliliters, does the student have left in the bottle?

Before the soccer practice, she drank 25 % of the water

25% of the water = 25% of 500

                             = 25% × 500

                              =\frac{25}{100} ×  500

At the right hand-side of the equation, the two zeros will cancel-out the other two zeros, hence;

                                = 25 × 5

                                 =125

25% of the water = 125 milliliters

From the question, it was said that drank 25% of the water before soccer, this implies that she drank 125 milliliters from the water bottles.

If she drank 125 milliliters of  from a 500 milliliters water contain in the water bottle, then the amount of water left will be 500 ml - 125 ml = 375 ml

This implies that before the soccer practice she had 375 milliliters of water left in the water bottle.

After the practice, she drank 1/3 of the remaining water, which means after the practice she drank 1/3 of 375

1/3 of 375 = \frac{1}{3} × 375 = \frac{375}{3} = 125

After the practice she drank 125 milliliters of water from her 375 milliliters water.

The amount of water she have left after the practice will be;

375 milliliters - 125 milliliters = 250 milliliters

Therefore, the amount of water the student have left in the bottle is 250 milliliters

8 0
3 years ago
Five less than the product of 7 and a number is equal to 3.
mr Goodwill [35]

Answer:

x = 8/7

Step-by-step explanation:

Step 1: Convert to math

7x - 5 = 3

Step 2: Solve for <em>x</em>

  1. Add to both sides: 7x = 8
  2. Divide both sides by 7: x = 8/7
6 0
3 years ago
An exponential function f(x) = ab^xpasses through the points (0, 2) and (3, 54). What are the values of a and
Vsevolod [243]

Answers:

a = 2

b = 3

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

Explanation:

Plug in x = 0 and y = 2 to find that

y = a*b^x

2 = a*b^0

2 = a*1

2 = a

a = 2

Then plug in x = 3 and y = 54 to determine the value of b

y = a*b^x

y = 2*b^x

54 = 2*b^3

2b^3 = 54

b^3 = 54/2

b^3 = 27

b = (27)^(1/3)

b = 3

So we have y = a*b^x update to y = 2*3^x

7 0
3 years ago
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