Question
Which of the following ordered pairs is in the solution set for y=8x−1
?(1 point)
Responses
(2,82)
open paren 2 comma 82 close paren - no response given
(2,81)
open paren 2 comma 81 close paren - no response given
(2,16)
open paren 2 comma 16 close paren - incorrect
(2,15)
?(1 point)
Responses
(2,82)
open paren 2 comma 82 close paren - no response given
(2,81)
open paren 2 comma 81 close paren - no response given
(2,16)
open paren 2 comma 16 close paren - incorrect
(2,15)
Answers
Answer
A line passes through the points (−4,−7)
and (2,−15)
. What is the equation of this line in point-slope form?(1 point)
Responses
y+7=−4/3(x+4)
y plus 7 equals negative Start Fraction 4 over 3 End Fraction left parenthesis x plus 4 right parenthesis
y−7=4/3(x−4)
y minus 7 equals Start Fraction 4 over 3 End Fraction left parenthesis x minus 4 right parenthesis
y−7=−4/3(x−4)
y minus 7 equals negative Start Fraction 4 over 3 End Fraction left parenthesis x minus 4 right parenthesis
y+7=4/3(x+4)
and (2,−15)
. What is the equation of this line in point-slope form?(1 point)
Responses
y+7=−4/3(x+4)
y plus 7 equals negative Start Fraction 4 over 3 End Fraction left parenthesis x plus 4 right parenthesis
y−7=4/3(x−4)
y minus 7 equals Start Fraction 4 over 3 End Fraction left parenthesis x minus 4 right parenthesis
y−7=−4/3(x−4)
y minus 7 equals negative Start Fraction 4 over 3 End Fraction left parenthesis x minus 4 right parenthesis
y+7=4/3(x+4)
Answer
A line with m=4
passes through the point (−7,−2)
. What is the equation of the line in slope-intercept form?(1 point)
Responses
y=−4x−2
y equals negative 4 x minus 2
y=4x−7
y equals 4 x minus 7
y=−4x−30
y equals negative 4 x minus 30
y=4x+26
passes through the point (−7,−2)
. What is the equation of the line in slope-intercept form?(1 point)
Responses
y=−4x−2
y equals negative 4 x minus 2
y=4x−7
y equals 4 x minus 7
y=−4x−30
y equals negative 4 x minus 30
y=4x+26
Answer
A line passes through the points (−20,16)
and (10,4)
. What is the equation of the line in standard form?(1 point)
Responses
y=−25x+8
y equals negative Start Fraction 2 over 5 End Fraction x plus 8
2x+5y=8
2 x plus 5 y equals 8
x+5y=40
x plus 5 y equals 40
2x+5y=40
and (10,4)
. What is the equation of the line in standard form?(1 point)
Responses
y=−25x+8
y equals negative Start Fraction 2 over 5 End Fraction x plus 8
2x+5y=8
2 x plus 5 y equals 8
x+5y=40
x plus 5 y equals 40
2x+5y=40
Answer
Use the table to answer the question.
x y
1 7
2 15
3 23
Use the data from the table to determine the slope of the line.
(1 point)
Responses
−8
negative 8
8
8
1/8
Start Fraction 1 over 8 End Fraction
−1/8
x y
1 7
2 15
3 23
Use the data from the table to determine the slope of the line.
(1 point)
Responses
−8
negative 8
8
8
1/8
Start Fraction 1 over 8 End Fraction
−1/8
Answer
Nate has a part-time job at the car wash. He earns $13 an hour, and he gets a weekly bonus of $100 if the business meets the quota of cars for the week. Assuming Nate gets his bonus, write a linear equation in slope-intercept form to represent how much Nate will get paid for the week if he works x hours over the week. Let y represent the amount he gets paid for the week and x represent the number of hours he works for the week.(1 point)
Responses
13x−y=−100
13 x minus y equals negative 100
y=13x+100
y equals 13 x plus 100
y=100x+13
y equals 100 x plus 13
y=13x
Responses
13x−y=−100
13 x minus y equals negative 100
y=13x+100
y equals 13 x plus 100
y=100x+13
y equals 100 x plus 13
y=13x
Answered by
GPT-4o mini
To determine which of the ordered pairs is in the solution set for the equation \(y = 8x - 1\), we will substitute \(x = 2\) into the equation and calculate the corresponding value of \(y\).
Substituting \(x = 2\):
\[
y = 8(2) - 1
\]
\[
y = 16 - 1
\]
\[
y = 15
\]
So, when \(x = 2\), \(y\) is \(15\).
Now we can check the ordered pairs:
- For \((2, 82)\): \(y = 82\) (not a solution)
- For \((2, 81)\): \(y = 81\) (not a solution)
- For \((2, 16)\): \(y = 16\) (not a solution)
- For \((2, 15)\): \(y = 15\) (this is a solution)
The ordered pair in the solution set for \(y = 8x - 1\) is \((2, 15)\).
Substituting \(x = 2\):
\[
y = 8(2) - 1
\]
\[
y = 16 - 1
\]
\[
y = 15
\]
So, when \(x = 2\), \(y\) is \(15\).
Now we can check the ordered pairs:
- For \((2, 82)\): \(y = 82\) (not a solution)
- For \((2, 81)\): \(y = 81\) (not a solution)
- For \((2, 16)\): \(y = 16\) (not a solution)
- For \((2, 15)\): \(y = 15\) (this is a solution)
The ordered pair in the solution set for \(y = 8x - 1\) is \((2, 15)\).
Answered by
GPT-4o mini
To find the equation of the line passing through the points \((-4, -7)\) and \((2, -15)\) in point-slope form, we first need to calculate the slope of the line. The formula for the slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substituting the points \((-4, -7)\) and \((2, -15)\):
- \(x_1 = -4\), \(y_1 = -7\)
- \(x_2 = 2\), \(y_2 = -15\)
Now we calculate:
\[
m = \frac{-15 - (-7)}{2 - (-4)} = \frac{-15 + 7}{2 + 4} = \frac{-8}{6} = -\frac{4}{3}
\]
Now, we can use the point-slope form of a line, which is given by:
\[
y - y_1 = m(x - x_1)
\]
Using point \((-4, -7)\) and the slope \(m = -\frac{4}{3}\):
\[
y - (-7) = -\frac{4}{3}(x - (-4))
\]
This simplifies to:
\[
y + 7 = -\frac{4}{3}(x + 4)
\]
Thus, the equation of the line in point-slope form is:
\[
y + 7 = -\frac{4}{3}(x + 4)
\]
From the provided options, the correct one is:
**y + 7 = -\frac{4}{3}(x + 4)**.
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substituting the points \((-4, -7)\) and \((2, -15)\):
- \(x_1 = -4\), \(y_1 = -7\)
- \(x_2 = 2\), \(y_2 = -15\)
Now we calculate:
\[
m = \frac{-15 - (-7)}{2 - (-4)} = \frac{-15 + 7}{2 + 4} = \frac{-8}{6} = -\frac{4}{3}
\]
Now, we can use the point-slope form of a line, which is given by:
\[
y - y_1 = m(x - x_1)
\]
Using point \((-4, -7)\) and the slope \(m = -\frac{4}{3}\):
\[
y - (-7) = -\frac{4}{3}(x - (-4))
\]
This simplifies to:
\[
y + 7 = -\frac{4}{3}(x + 4)
\]
Thus, the equation of the line in point-slope form is:
\[
y + 7 = -\frac{4}{3}(x + 4)
\]
From the provided options, the correct one is:
**y + 7 = -\frac{4}{3}(x + 4)**.
Answered by
GPT-4o mini
To find the equation of a line in slope-intercept form (which is \(y = mx + b\)), we start with the given slope \(m = 4\) and the point \((-7, -2)\).
Using the point-slope form of the equation, we can find the intercept \(b\) as follows:
1. Start with the slope-intercept form:
\[
y = mx + b
\]
2. Substitute \(m = 4\) and the point \((-7, -2)\) into the equation:
\[
-2 = 4(-7) + b
\]
3. Calculate \(4(-7)\):
\[
-2 = -28 + b
\]
4. Solve for \(b\):
\[
b = -2 + 28
\]
\[
b = 26
\]
Now that we have \(m\) and \(b\), we can write the equation of the line:
\[
y = 4x + 26
\]
From the provided options, the correct answer is:
**y = 4x + 26**.
Using the point-slope form of the equation, we can find the intercept \(b\) as follows:
1. Start with the slope-intercept form:
\[
y = mx + b
\]
2. Substitute \(m = 4\) and the point \((-7, -2)\) into the equation:
\[
-2 = 4(-7) + b
\]
3. Calculate \(4(-7)\):
\[
-2 = -28 + b
\]
4. Solve for \(b\):
\[
b = -2 + 28
\]
\[
b = 26
\]
Now that we have \(m\) and \(b\), we can write the equation of the line:
\[
y = 4x + 26
\]
From the provided options, the correct answer is:
**y = 4x + 26**.
Answered by
GPT-4o mini
To determine the equation of the line in standard form that passes through the points \((-20, 16)\) and \( (10, 4)\), we need to find the slope and then use one of the points to express the equation in standard form.
### Step 1: Calculate the slope (m)
The formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substituting the points \((-20, 16)\) and \((10, 4)\):
- \(x_1 = -20\), \(y_1 = 16\)
- \(x_2 = 10\), \(y_2 = 4\)
Now calculate the slope:
\[
m = \frac{4 - 16}{10 - (-20)} = \frac{-12}{30} = -\frac{2}{5}
\]
### Step 2: Use the slope and one point to find the equation
Using the point-slope form \(y - y_1 = m(x - x_1)\) with \((-20, 16)\):
\[
y - 16 = -\frac{2}{5}(x + 20)
\]
Distributing the slope:
\[
y - 16 = -\frac{2}{5}x - \frac{40}{5}
\]
\[
y - 16 = -\frac{2}{5}x - 8
\]
Now, add 16 to both sides:
\[
y = -\frac{2}{5}x + 8
\]
### Step 3: Convert to standard form
Standard form is typically written as \(Ax + By = C\). Let's convert \(y = -\frac{2}{5}x + 8\) into that form.
- We can multiply the entire equation by 5 to eliminate the fraction:
\[
5y = -2x + 40
\]
Rearranging gives:
\[
2x + 5y = 40
\]
So the standard form of the equation of the line passing through the given points is:
**2x + 5y = 40**.
### Step 1: Calculate the slope (m)
The formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substituting the points \((-20, 16)\) and \((10, 4)\):
- \(x_1 = -20\), \(y_1 = 16\)
- \(x_2 = 10\), \(y_2 = 4\)
Now calculate the slope:
\[
m = \frac{4 - 16}{10 - (-20)} = \frac{-12}{30} = -\frac{2}{5}
\]
### Step 2: Use the slope and one point to find the equation
Using the point-slope form \(y - y_1 = m(x - x_1)\) with \((-20, 16)\):
\[
y - 16 = -\frac{2}{5}(x + 20)
\]
Distributing the slope:
\[
y - 16 = -\frac{2}{5}x - \frac{40}{5}
\]
\[
y - 16 = -\frac{2}{5}x - 8
\]
Now, add 16 to both sides:
\[
y = -\frac{2}{5}x + 8
\]
### Step 3: Convert to standard form
Standard form is typically written as \(Ax + By = C\). Let's convert \(y = -\frac{2}{5}x + 8\) into that form.
- We can multiply the entire equation by 5 to eliminate the fraction:
\[
5y = -2x + 40
\]
Rearranging gives:
\[
2x + 5y = 40
\]
So the standard form of the equation of the line passing through the given points is:
**2x + 5y = 40**.
Answered by
GPT-4o mini
To determine the slope of the line using the points provided in the table, we can use the slope formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Let's use the points \((1, 7)\) and \((2, 15)\):
- For \(x_1 = 1\), \(y_1 = 7\)
- For \(x_2 = 2\), \(y_2 = 15\)
Now, we can calculate the slope (\(m\)):
\[
m = \frac{15 - 7}{2 - 1} = \frac{8}{1} = 8
\]
Alternatively, we can also find the slope using the next pair, \((2, 15)\) and \((3, 23)\):
- For \(x_1 = 2\), \(y_1 = 15\)
- For \(x_2 = 3\), \(y_2 = 23\)
Calculating the slope:
\[
m = \frac{23 - 15}{3 - 2} = \frac{8}{1} = 8
\]
In both cases, the slope is the same.
Thus, the slope of the line is:
**8**.
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Let's use the points \((1, 7)\) and \((2, 15)\):
- For \(x_1 = 1\), \(y_1 = 7\)
- For \(x_2 = 2\), \(y_2 = 15\)
Now, we can calculate the slope (\(m\)):
\[
m = \frac{15 - 7}{2 - 1} = \frac{8}{1} = 8
\]
Alternatively, we can also find the slope using the next pair, \((2, 15)\) and \((3, 23)\):
- For \(x_1 = 2\), \(y_1 = 15\)
- For \(x_2 = 3\), \(y_2 = 23\)
Calculating the slope:
\[
m = \frac{23 - 15}{3 - 2} = \frac{8}{1} = 8
\]
In both cases, the slope is the same.
Thus, the slope of the line is:
**8**.
Answered by
GPT-4o mini
To create a linear equation in slope-intercept form that represents Nate's weekly earnings based on the hours he works and his bonus, we need to account for both components:
1. **Hourly pay**: Nate earns $13 for each hour he works, which can be represented as \(13x\), where \(x\) is the number of hours he works.
2. **Bonus**: He receives a bonus of $100 if the business meets the quota.
Incorporating both components, his total pay, represented as \(y\), can be expressed as:
\[
y = 13x + 100
\]
Here:
- \(y\) is the total weekly pay,
- \(13x\) represents the earnings from hours worked, and
- \(100\) represents the bonus.
Thus, the linear equation in slope-intercept form is:
**y = 13x + 100**.
1. **Hourly pay**: Nate earns $13 for each hour he works, which can be represented as \(13x\), where \(x\) is the number of hours he works.
2. **Bonus**: He receives a bonus of $100 if the business meets the quota.
Incorporating both components, his total pay, represented as \(y\), can be expressed as:
\[
y = 13x + 100
\]
Here:
- \(y\) is the total weekly pay,
- \(13x\) represents the earnings from hours worked, and
- \(100\) represents the bonus.
Thus, the linear equation in slope-intercept form is:
**y = 13x + 100**.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.