Question
Compare Linear Function 1 with Linear Function 2. Which one has the lesser rate of change? Choose 1 for Linear Function 1; Choose 2 for Linear Function 2.
Linear Function 1: y=7x+4
Linear Function 2:
x y
10 61
12 73
Linear Function 1: y=7x+4
Linear Function 2:
x y
10 61
12 73
Answers
Answer
Use the image to answer the question.
A coordinate plane with four quadrants shows the x-axis ranging from negative 7 to 4 in increments of 1, and the y-axis ranging from negative 9 to 8 in increments of 1. An upward line with arrows at both the ends is shown on the plane. The line passes through the first, second, and third quadrants. The line intersects the x-axis at left parenthesis negative 1.5 comma 0 right parenthesis and the y-axis at left parenthesis 0 comma 3 right parenthesis.
Sekou sketched the graph shown based on a verbal description. Fill in the blanks to tell what information she was likely given.
A coordinate plane with four quadrants shows the x-axis ranging from negative 7 to 4 in increments of 1, and the y-axis ranging from negative 9 to 8 in increments of 1. An upward line with arrows at both the ends is shown on the plane. The line passes through the first, second, and third quadrants. The line intersects the x-axis at left parenthesis negative 1.5 comma 0 right parenthesis and the y-axis at left parenthesis 0 comma 3 right parenthesis.
Sekou sketched the graph shown based on a verbal description. Fill in the blanks to tell what information she was likely given.
Answer
What is the initial value?
Answer
The function has a constant rate of change equal to ___
Answer
Use the image to answer the question.
A coordinate plane shows the x-axis ranging from negative 1 to 11 in increments of 1, and the y-axis ranging from negative 1 to 14 in increments of 1. The first quadrant shows 2 plotted points connected by an inverted parabola. The x-axis represents the Horizontal Distance from Lucas in Feet, and the y-axis represents the Height Above the Ground in Feet. A closed point is plotted at left parenthesis 0 comma 4 right parenthesis. Another closed point is plotted at left parenthesis 10 comma 0 right parenthesis. A curved line connects the two endpoints with the vertex at left parenthesis 4.5 comma 13 right parenthesis.
Antonio sketched the graph shown based on a verbal description. Fill in the blanks to tell what information he was likely given.
Lucas threw a ball up into the air from a height of __ feet. The ball reached a maximum height of 13 feet when it was a horizontal distance of 4.5 feet from Lucas. The ball landed on the ground __ feet from Lucas.
A coordinate plane shows the x-axis ranging from negative 1 to 11 in increments of 1, and the y-axis ranging from negative 1 to 14 in increments of 1. The first quadrant shows 2 plotted points connected by an inverted parabola. The x-axis represents the Horizontal Distance from Lucas in Feet, and the y-axis represents the Height Above the Ground in Feet. A closed point is plotted at left parenthesis 0 comma 4 right parenthesis. Another closed point is plotted at left parenthesis 10 comma 0 right parenthesis. A curved line connects the two endpoints with the vertex at left parenthesis 4.5 comma 13 right parenthesis.
Antonio sketched the graph shown based on a verbal description. Fill in the blanks to tell what information he was likely given.
Lucas threw a ball up into the air from a height of __ feet. The ball reached a maximum height of 13 feet when it was a horizontal distance of 4.5 feet from Lucas. The ball landed on the ground __ feet from Lucas.
Answered by
GPT 3.5
To find the rate of change for each function, we can calculate the difference in y values over the difference in x values.
For Linear Function 1:
Rate of change = (73-61)/(12-10) = 12/2 = 6
For Linear Function 2:
Rate of change = (73-61)/(12-10) = 12/2 = 6
Based on the calculations above, both linear functions have the same rate of change, which is 6.
For Linear Function 1:
Rate of change = (73-61)/(12-10) = 12/2 = 6
For Linear Function 2:
Rate of change = (73-61)/(12-10) = 12/2 = 6
Based on the calculations above, both linear functions have the same rate of change, which is 6.
Answered by
GPT 3.5
Based on the sketch of the graph provided, Sekou was likely given the following information for the linear function:
1. The line passes through the points (-1.5, 0) and (0, 3).
2. The line intersects the x-axis at (-1.5, 0) and the y-axis at (0, 3).
3. The line passes through the first, second, and third quadrants.
4. The line is upward-sloping.
1. The line passes through the points (-1.5, 0) and (0, 3).
2. The line intersects the x-axis at (-1.5, 0) and the y-axis at (0, 3).
3. The line passes through the first, second, and third quadrants.
4. The line is upward-sloping.
Answered by
GPT 3.5
In the linear function provided, the initial value is the y-intercept, which is the value of y when x is equal to 0.
From the information given, we know that the line intersects the y-axis at the point (0, 3).
Therefore, the initial value of the linear function is 3.
From the information given, we know that the line intersects the y-axis at the point (0, 3).
Therefore, the initial value of the linear function is 3.
Answered by
GPT 3.5
The constant rate of change of a linear function is equal to the slope of the line.
To calculate the slope, we can use the formula:
slope = (change in y) / (change in x)
From the information provided, we can calculate the slope using the points (0, 3) and (-1.5, 0):
slope = (3 - 0) / (0 - (-1.5))
slope = 3 / 1.5
slope = 2
Therefore, the constant rate of change of the linear function is 2.
To calculate the slope, we can use the formula:
slope = (change in y) / (change in x)
From the information provided, we can calculate the slope using the points (0, 3) and (-1.5, 0):
slope = (3 - 0) / (0 - (-1.5))
slope = 3 / 1.5
slope = 2
Therefore, the constant rate of change of the linear function is 2.
Answered by
GPT 3.5
Based on the sketch of the inverted parabola provided, Antonio was likely given the following information about Lucas throwing a ball:
- Lucas threw a ball up into the air from a height of 4 feet.
- The ball reached a maximum height of 13 feet when it was a horizontal distance of 4.5 feet from Lucas.
- The ball landed on the ground 10 feet from Lucas.
- Lucas threw a ball up into the air from a height of 4 feet.
- The ball reached a maximum height of 13 feet when it was a horizontal distance of 4.5 feet from Lucas.
- The ball landed on the ground 10 feet from Lucas.