24. a plane is flying at 1500 feet. it descends at 125 feet per second. the equation that models the plane’s elevation, y, in terms of the number of seconds, x that have passed is $y = -125x + 1500$. which of the following interpretations is correct?
a. the slope is 1500 feet and this is the initial height of the plane.
b. the slope is -125 feet/second and this is the initial height of the plane.
c. the slope is 1500 feet/second and this is the rate at which the plane is descending.
d. the slope is -125 feet/second and this the rate at which the plane is descending.

25. what are the x-intercept and the y-intercept of the linear equation $3x - y = 6$?
a) x-intercept = (0, 6), y-intercept = (2, 0)
c) x-intercept = (0, 2), y-intercept (-6, 0)
b) x-intercept = (2, 0), y-intercept = (0, -6)
d) x-intercept = (-6, 2), y-intercept (2, -6)

26. what is the slope of the line passing through (3, 5) and (1, 4).
a) $\frac{1}{2}$
b) $-\frac{1}{2}$
c) 2
d) -2

27. what is the slope and y-intercept of the linear equation $9x - 3y = 15$?
a) slope = -4 y-intercept = 8
b) slope = 3 y-intercept = -5
c) slope = 2 y-intercept = 10
d) slope = -3 y-intercept = 5

28. write an equation for the line that passes through the point (-2, 4) and has a slope of -5.
a) $y = -5x + 14$
b) $y = -5x + 4$
c) $y = -5x - 2$
d) $y = -5x - 6$

29. a scatterplot and its line of best fit are shown. using the line of best fit, which statement regarding the rate of change is true?
a. for every hour you exercise, your resting heart rate increases by approximately 5 beats per minute
b. increasing exercise does not affect your resting heart rate
c. for every hour you exercise, your resting heart rate reduces by approximately 4 beats per minute
d. for every hour you exercise, your resting heart rate reduces approximately 15 beats per minute

Question

24. a plane is flying at 1500 feet. it descends at 125 feet per second. the equation that models the plane’s elevation, y, in terms of the number of seconds, x that have passed is $y = -125x + 1500$. which of the following interpretations is correct?
a. the slope is 1500 feet and this is the initial height of the plane.
b. the slope is -125 feet/second and this is the initial height of the plane.
c. the slope is 1500 feet/second and this is the rate at which the plane is descending.
d. the slope is -125 feet/second and this the rate at which the plane is descending.

25. what are the x-intercept and the y-intercept of the linear equation $3x - y = 6$?
a) x-intercept = (0, 6), y-intercept = (2, 0)
c) x-intercept = (0, 2), y-intercept (-6, 0)
b) x-intercept = (2, 0), y-intercept = (0, -6)
d) x-intercept = (-6, 2), y-intercept (2, -6)

26. what is the slope of the line passing through (3, 5) and (1, 4).
a) $\frac{1}{2}$
b) $-\frac{1}{2}$
c) 2
d) -2

27. what is the slope and y-intercept of the linear equation $9x - 3y = 15$?
a) slope = -4  y-intercept = 8
b) slope = 3  y-intercept = -5
c) slope = 2  y-intercept = 10
d) slope = -3  y-intercept = 5

28. write an equation for the line that passes through the point (-2, 4) and has a slope of -5.
a) $y = -5x + 14$
b) $y = -5x + 4$
c) $y = -5x - 2$
d) $y = -5x - 6$

29. a scatterplot and its line of best fit are shown. using the line of best fit, which statement regarding the rate of change is true?
a. for every hour you exercise, your resting heart rate increases by approximately 5 beats per minute
b. increasing exercise does not affect your resting heart rate
c. for every hour you exercise, your resting heart rate reduces by approximately 4 beats per minute
d. for every hour you exercise, your resting heart rate reduces approximately 15 beats per minute

Accepted Answer

### Question 24
# Explanation:
## Step1: Recall slope-intercept form
The slope - intercept form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept (initial value when $x = 0$).
In the equation $y=-125x + 1500$, $m=-125$ and $b = 1500$.

## Step2: Analyze the slope and y - intercept
The slope $m=-125$ represents the rate of change of $y$ with respect to $x$. Since $y$ is the elevation and $x$ is the time in seconds, the slope of $- 125$ feet per second represents the rate at which the plane is descending (because the elevation is decreasing as time increases). The y - intercept $b = 1500$ is the initial height of the plane (when $x = 0$, the time is 0 seconds, so the elevation is 1500 feet).

Now let's analyze each option:
- Option A: The slope is not 1500, the y - intercept is 1500 (initial height). So A is incorrect.
- Option B: The slope is - 125 feet per second, but the initial height is the y - intercept (1500), not the slope. So B is incorrect.
- Option C: The slope is not 1500 feet per second. The slope is - 125 feet per second (rate of descent). So C is incorrect.
- Option D: The slope is - 125 feet per second and it represents the rate at which the plane is descending. This is correct.

# Answer: D. The slope is -125 feet/second and this the rate at which the plane is descending.

### Question 25
# Explanation:
## Step1: Find the x - intercept
To find the x - intercept, we set $y = 0$ in the equation $3x-y=6$.
Substitute $y = 0$ into the equation:
$3x-0=6$
$3x=6$
Divide both sides by 3: $x=\frac{6}{3}=2$. So the x - intercept is $(2,0)$ (since when $y = 0$, $x = 2$).

## Step2: Find the y - intercept
To find the y - intercept, we set $x = 0$ in the equation $3x - y=6$.
Substitute $x = 0$ into the equation:
$3(0)-y=6$
$-y=6$
Multiply both sides by - 1: $y=-6$. So the y - intercept is $(0,-6)$.

Now let's check the options:
- Option A: x - intercept is wrong (should be (2,0) not (0,6)) and y - intercept is wrong (should be (0, - 6) not (2,0)). So A is incorrect.
- Option B: x - intercept is (2,0) and y - intercept is (0, - 6). This is correct.
- Option C: x - intercept is wrong (should be (2,0) not (0,2)) and y - intercept is wrong (should be (0, - 6) not (-6,0)). So C is incorrect.
- Option D: Both x - intercept and y - intercept are wrong. So D is incorrect.

# Answer: B) x-intercept = (2, 0), y-intercept = (0, -6)

### Question 26
# Explanation:
## Step1: Recall the slope formula
The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by the formula $m=\frac{y_2 - y_1}{x_2 - x_1}$.

## Step2: Identify the points
We have the points $(x_1,y_1)=(3,5)$ and $(x_2,y_2)=(1,4)$.

## Step3: Calculate the slope
Substitute the values into the slope formula:
$m=\frac{4 - 5}{1 - 3}=\frac{-1}{-2}=\frac{1}{2}$

Now let's check the options:
- Option A: $\frac{1}{2}$ is the slope we calculated. So A is correct.
- Option B: The slope is not $-\frac{1}{2}$. So B is incorrect.
- Option C: The slope is not 2. So C is incorrect.
- Option D: The slope is not - 2. So D is incorrect.

# Answer: A) $\frac{1}{2}$

### Question 27
# Explanation:
## Step1: Rewrite the equation in slope - intercept form
We start with the equation $9x-3y = 15$.
First, solve for $y$:
$-3y=-9x + 15$
Divide each term by - 3: $y=\frac{-9x}{-3}+\frac{15}{-3}$
$y = 3x-5$

## Step2: Identify the slope and y - intercept
In the slope - intercept form $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept.
For $y = 3x-5$, the slope $m = 3$ and the y - intercept $b=-5$.

Now let's check the options:
- Option A: Slope is not - 4 and y - intercept is not 8. So A is incorrect.
- Option B: Slope is 3 and y - intercept is - 5. This is correct.
- Option C: Slope is not 2 and y - intercept is not 10. So C is incorrect.
- Option D: Slope is not - 3 and y - intercept is not 5. So D is incorrect.

# Answer: B) slope = 3  y-intercept = -5

### Question 28
# Explanation:
## Step1: Recall the point - slope form
The point - slope form of a linear equation is $y - y_1=m(x - x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope.

## Step2: Substitute the values
We have the point $(x_1,y_1)=(-2,4)$ and $m=-5$.
Substitute into the point - slope form:
$y - 4=-5(x-(-2))$
$y - 4=-5(x + 2)$

## Step3: Simplify the equation
Expand the right - hand side: $y-4=-5x-10$
Add 4 to both sides: $y=-5x-10 + 4$
$y=-5x-6$? Wait, no, wait:
Wait, $y-4=-5(x + 2)$
$y-4=-5x-10$
$y=-5x-10 + 4$
$y=-5x-6$? No, wait,  $-10 + 4=-6$? Wait, no, let's recalculate:
$y-4=-5x-10$
$y=-5x-10 + 4$
$y=-5x-6$? Wait, no, that's wrong. Wait, $-10+4=-6$? Wait, no, the correct calculation:
$y-4=-5(x + 2)$
$y-4=-5x-10$
Add 4 to both sides: $y=-5x-10 + 4$
$y=-5x-6$? Wait, no, the correct answer should be $y=-5x-6$? Wait, no, let's check again.
Wait, the point is $(-2,4)$ and slope $m = - 5$.
Using $y=mx + b$, substitute $x=-2$, $y = 4$ and $m=-5$ into $y=mx + b$:
$4=-5\times(-2)+b$
$4 = 10 + b$
Subtract 10 from both sides: $b=4 - 10=-6$
So the equation is $y=-5x-6$? Wait, no, wait:
Wait, $y=mx + b$, $m=-5$, $x=-2$, $y = 4$
$4=-5\times(-2)+b$
$4 = 10 + b$
$b=4 - 10=-6$
So $y=-5x-6$? But let's check the options:
Option A: $y=-5x + 14$, Option B: $y=-5x + 4$, Option C: $y=-5x-2$, Option D: $y=-5x-6$
Wait, I made a mistake earlier. Let's do it again.
Point - slope form: $y - y_1=m(x - x_1)$
$x_1=-2$, $y_1 = 4$, $m=-5$
$y - 4=-5(x-(-2))=y - 4=-5(x + 2)$
$y-4=-5x-10$
$y=-5x-10 + 4$
$y=-5x-6$
So the correct equation is $y=-5x-6$, which is option D? Wait, no, wait, the options are:
A) $y=-5x + 14$
B) $y=-5x + 4$
C) $y=-5x-2$
D) $y=-5x-6$
Wait, but when $x=-2$, let's check option D: $y=-5\times(-2)-6=10 - 6 = 4$, which matches the point $(-2,4)$.
Wait, but let's check the calculation of $b$ again.
Using $y=mx + b$, $m=-5$, $x=-2$, $y = 4$:
$4=-5\times(-2)+b$
$4 = 10 + b$
$b=4 - 10=-6$
So the equation is $y=-5x-6$, which is option D.

Wait, but let's check the options again. The options are:
A) $y=-5x + 14$
B) $y=-5x + 4$
C) $y=-5x-2$
D) $y=-5x-6$

So the correct answer is D? Wait, no, I think I made a mistake in the sign when expanding. Let's re - expand $y - 4=-5(x + 2)$:
$y-4=-5x-10$
$y=-5x-10 + 4$
$y=-5x-6$
Yes, so the correct equation is $y=-5x-6$, which is option D.

Now let's check each option:
- Option A: When $x=-2$, $y=-5\times(-2)+14 = 10 + 14 = 24
eq4$. So A is incorrect.
- Option B: When $x=-2$, $y=-5\times(-2)+4 = 10 + 4 = 14
eq4$. So B is incorrect.
- Option C: When $x=-2$, $y=-5\times(-2)-2 = 10 - 2 = 8
eq4$. So C is incorrect.
- Option D: When $x=-2$, $y=-5\times(-2)-6 = 10 - 6 = 4$, which matches the point $(-2,4)$. So D is correct.

# Answer: D) $y=-5x-6$

### Question 29
# Explanation:
## Step1: Analyze the scatter plot and line of best fit
The line of best fit in the scatter plot has a negative slope (since as the number of hours of exercise per week (x - variable) increases, the resting heart rate (y - variable) decreases).

## Step2: Analyze each option
- Option A: The slope is negative, so the resting heart rate should decrease, not increase. So A is incorrect.
- Option B: The line of best fit has a non - zero slope, so exercise does affect the resting heart rate. So B is incorrect.
- Option C: To find the rate of change, we can look at two points on the line of best fit. For example, when $x = 0$, $y\approx80$ and when $x = 5$, $y\approx60$. The slope $m=\frac{60 - 80}{5 - 0}=\frac{-20}{5}=-4$. So for every hour of exercise, the resting heart rate reduces by approximately 4 beats per minute. So C is correct.
- Option D: The rate of change is approximately - 4 (a decrease of 4 beats per minute per hour of exercise), not - 15. So D is incorrect.

# Answer: C. For every hour you exercise, your resting heart rate reduces by approximately 4 beats per minute

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Question 24

Step1: Recall slope-intercept form

Step2: Analyze the slope and y - intercept

Step1: Find the x - intercept

Step2: Find the y - intercept

Step1: Recall the slope formula

Step2: Identify the points

Step3: Calculate the slope

Answer:

Question 25