Question

A)
Which equation represents the line that passes through the points (6, –3) and (–4, –9)?
(1 point)
y + 4 = 3/5 (x + 9)
y + 4 = 5/3 (x + 9)
y - 3 = 3/5 (x + 6)
y + 3 = 3/5 (x – 6)

Answer 1

A)
The population of a city increases by 4,000 people each year. In 2025, the population is
projected to be 450,000 people. What is an equation that gives the city’s population p (in
thousands of people) x years after 2010?
(1 point)
p = 4x + 50
p – 450 = 4(x – 15)
p – 15 = 4(x – 450)
p = 4x + 15

Answer 2

which one though

Answer 3

that not a answer

Answer 4

To find the equation of the line that passes through two points, we can use the formula for the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.

First, let's find the slope of the line using the formula:

m = (y2 - y1) / (x2 - x1)

Using the points (6, -3) and (-4, -9), we have:

m = (-9 - (-3)) / (-4 - 6)
= (-9 + 3) / (-4 - 6)
= -6 / -10
= 3/5

Now that we have the slope, we can use either of the given equations to find the y-intercept. Let's use the equation y - 3 = 3/5 (x + 6):

Plugging in the coordinates of one of the points, (6, -3), gives us:

-3 - 3 = (3/5)(6 + 6)
-6 = 3/5 * 12
-6 = 36/5

To get the equation in the slope-intercept form (y = mx + b), we need to solve for y:

y = (3/5)x + b

We already found the y-intercept, which is -6:

y = (3/5)x - 6

Therefore, the equation that represents the line passing through the points (6, -3) and (-4, -9) is:

y = (3/5)x - 6

Answer 5

To find the equation that gives the city's population x years after 2010, we need to determine the starting population and the rate of increase.

In 2010, the population is the starting point, and we'll assume it is 0 since we are counting the population in thousands of people.

Next, we know that the population increases by 4,000 people each year. Since we are counting the population in thousands of people, the rate of increase would be 4.

Therefore, the equation that gives the city's population p (in thousands of people) x years after 2010 is:

p = 4x + 0

However, for clarity, we usually add the y-intercept term. In this case, since we assume the starting population in 2010 is 0, the equation becomes:

p = 4x + 0

Simplifying this equation gives the final answer:

p = 4x

Answer 6

I apologize for the confusion. The correct equation that gives the city's population p (in thousands of people) x years after 2010 is:

p = 4x + 0

However, for clarity, we usually add the y-intercept term. In this case, since we assume the starting population in 2010 is 0, the equation becomes:

p = 4x

So, the correct answer is p = 4x.

Answer 7

I apologize for the confusion. The correct equation that gives the city's population p (in thousands of people) x years after 2010 is:

p = 4x + 50

In this equation, the coefficient of x, which is 4, represents the rate of increase in the population each year. The equation is given as p = 4x + 50, where 50 represents the starting population in 2010, assumed to be 50,000 people (since we are counting the population in thousands of people).