Write the equation of the line, with the given properties, in the slope-intercept form.Slope= -3, through (-9,7)

What is the y-intercept of the equation y = 2x + 5

Harrizon [31]

y-intercept is at 5.

from y = mx+b

m is the slope

b is the y-intercept.

5 0

3 years ago

Read 2 more answers

4) The quantities x and y are in proportion x 4 30 8 __b__ a) b) c) y 6 45 __a__ 15 Find the value of a and b. Find the constant

Ivan

Question:

The quantities x and y are in proportion

x y

4 6

30 45

8 b

a 15

(a) Find the values of a and b.

(b) Find the constant of variation. Is it direct variation or inverse variation?

Answer:

$a = 10$ and $b = 12$

Constant of variation is 1.5

Direct Variation

Step-by-step explanation:

Solving (a): The values of a and b

First, we determine the equation that relates x and y

From the table, we have:

$(x_1,y_1) = (4,6)$

$(x_2,y_2) = (30,45)$

The slope (m) is:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

$m = \frac{45 - 6}{30 -4}$

$m = \frac{39}{26}$

$m = 1.5$

The equation is then calculated using:

$y - y_1 = m(x - x_1)$

This gives:

$y - 6 = 1.5(x - 4)$

$y - 6 = 1.5x - 6$

$y = 1.5x$

Solving for the value of b

From the table: x = 8, y = b

Substitute these values in $y = 1.5x$

$b = 1.5 * 8$

$b = 12$

Solving for the value of a

From the table: x = a, y = 15

Substitute these values in $y = 1.5x$

$15 = 1.5 * a$

Solve for a

$a = \frac{15}{1.5}$

$a = 10$

Solving (b): The constant of variation.

This has been solved in (a) above as:

$m = 1.5$

Direct or Inverse?

From the given table, we notice that y increases as x increases and y decreases as x decreases.

<em>This shows direct variation</em>

3 0

2 years ago

Suppose the average yearly salary of an individual whose final degree is a master's is $46 thousand less than twice that of an

seraphim [82]

Answer:

The average sallary of a Master's is 60 thousand and of a Bachellor's is 53 thousand.

Step-by-step explanation:

In order to solve this problem we first need to attribute variables to the unkown quantities. We will call the average salary of Master's "x" and the average salary of a Bachellor's "y". The first information the problem gives us is:

x = 2*y - 46

The second one is:

x + y = 113

We now have two equations and two variables, so we can solve the system. To do that we will use the value for x from the first equation on the second one. We have:

2*y - 46 + y = 113

3*y = 113 + 46

3*y = 159

y = 159/3 = 53

x = 2*(53) - 46 = 60

The average sallary of a Master's is 60 thousand and of a Bachellor's is 53 thousand.

3 0

3 years ago

Juan and his little brother Miquel ran around a circular track together. Juan ran on the inner track, which has a radius of 30 f

MArishka [77]

Answer:

he would have had to run 20 more feet then Juan

Step-by-step explanation:

5 0

3 years ago

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The expression 4x/5-2x/3 is equivalent to what?

Vinvika [58]

Answer:

(2 x)/15

Step-by-step explanation:

Simplify the following:

(4 x)/5 - (2 x)/3

Put each term in (4 x)/5 - (2 x)/3 over the common denominator 15: (4 x)/5 - (2 x)/3 = (12 x)/15 - (10 x)/15:

(12 x)/15 - (10 x)/15

(12 x)/15 - (10 x)/15 = (12 x - 10 x)/15:

(12 x - 10 x)/15

12 x - 10 x = 2 x:

Answer: (2 x)/15

7 0

3 years ago