Question

Which equation is equivalent to y – 6 = –12(x + 4)? (1 point)
y = –6x – 48 y = 6x – 48
y = –12x – 42 y = –12x – 54

Answer 1

Which point is located on the line represented by the equation y + 4 = – 5(x – 3)?
(1 point)
(–4, –5) (–5, –4) (3, –4) (–3, 4)

Answer 2

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 3

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 4

The equation that is equivalent to y – 6 = –12(x + 4) is y = –12x – 42.

Answer 5

To find which point is located on the line represented by the equation y + 4 = – 5(x – 3), we need to substitute the x and y values of each point option into the equation and check which one satisfies the equation.

Let's check each option:

Option 1: (–4, –5)
Substituting x = -4 and y = -5 into the equation: -5 + 4 = -5(-4 - 3) -> -1 = 35
This does not satisfy the equation.

Option 2: (–5, –4)
Substituting x = -5 and y = -4 into the equation: -4 + 4 = -5(-5 - 3) -> 0 = 40
This also does not satisfy the equation.

Option 3: (3, –4)
Substituting x = 3 and y = -4 into the equation: -4 + 4 = -5(3 - 3) -> 0 = 0
This satisfies the equation.

Option 4: (–3, 4)
Substituting x = -3 and y = 4 into the equation: 4 + 4 = -5(-3 - 3) -> 8 = 24
This does not satisfy the equation.

Therefore, the point (3, -4) is located on the line represented by the equation y + 4 = –5(x – 3).

Answer 6

To determine the equation that represents the line passing through the points (6, -3) and (-4, -9), we can use the point-slope form:

y - y1 = m(x - x1)

where m is the slope of the line and (x1, y1) are the coordinates of one of the given points.

First, let's find the slope (m):

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

m = (-9 - (-3)) / (-4 - 6)

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

m = (-6) / (-10)

m = 3/5

Next, we can use one of the given points (6, -3) in the point-slope form:

y - (-3) = (3/5)(x - 6)

Simplifying:

y + 3 = (3/5)(x - 6)

This equation is equivalent to y + 3 = (3/5)x - 18/5.

To get rid of the fraction, let's multiply both sides by 5:

5(y + 3) = 3x - 18

5y + 15 = 3x - 18

Rearranging the equation:

5y = 3x - 33

Finally, subtracting 3x from both sides:

-3x + 5y = -33

Therefore, the equation that represents the line passing through the points (6, -3) and (-4, -9) is -3x + 5y = -33.

Answer 7

To find an equation that gives the city's population p (in thousands of people) x years after 2010, we need to consider the initial population in 2010 and the growth rate.

In 2010, the population is the base population. Let's denote it as P0.

Each year, the population increases by 4,000 people. Therefore, the growth rate is 4,000 people/year.

To find the base population P0, we can subtract the total increase in population from the projected population in 2025.

Projected population in 2025 = 450,000 people
Total increase in population from 2010 to 2025 = 4,000 people/year * (2025 - 2010) years = 4,000 * 15 = 60,000 people
Base population in 2010 = Projected population in 2025 - Total increase in population from 2010 to 2025 = 450,000 - 60,000 = 390,000 people

Now, let's denote x as the number of years after 2010. The equation that gives the city's population p (in thousands of people) x years after 2010 can be expressed as:

p = 4x + 390

However, since the question asks for the population in thousands of people, we divide both sides of the equation by 1,000:

p/1,000 = (4x + 390)/1,000

Simplifying the equation:

p = 0.004x + 0.39

Therefore, the equation that gives the city's population p (in thousands of people) x years after 2010 is p = 0.004x + 0.39 (which can also be written as p = 4x + 390).