Use the table to answer the question.
($) Cost of Candy Bar A
Quantity ($) Cost
1 1.25
2 2.50
3 3.75
4 5.00
5 6.25
The cost of Candy Bar A is displayed in the table. The proportional relationship between the cost and quantity for Candy Bar B is represented by the equation y=x . Which candy bar is the cheapest cost per bar? Enter 1 for Candy Bar A. Enter 2 for Candy Bar B.
Since the cost of Candy Bar A is linearly increasing based on the quantity, we can see that the cost per bar for Candy Bar A is $1.25 when buying one, $1.25/1= $1.25.
For Candy Bar B, the cost per bar is the same as the quantity, so the cost per bar for Candy Bar B is always equal to the quantity.
Therefore, Candy Bar B is the cheapest cost per bar as the cost per bar is always equal to the quantity. Enter 2 for Candy Bar B.
Use the image to answer the question.
An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid upward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma negative 2 right parenthesis and left parenthesis 1 comma 3 right parenthesis.
Use the graph to derive the equation of the line in slope-intercept form.
(1 point)
To find the equation of the line in slope-intercept form, we need to first find the slope of the line. The slope is given by the formula:
m = (change in y) / (change in x)
Given the two points (0, -2) and (1, 3), the change in y = 3 - (-2) = 5 and the change in x = 1 - 0 = 1.
So, the slope (m) is:
m = 5 / 1 = 5
Now that we have the slope, we can use one of the points to find the y-intercept (b). Let's use the point (0, -2).
y = mx + b
-2 = 5(0) + b
-2 = b
So, the y-intercept (b) is -2.
Therefore, the equation of the line in slope-intercept form is:
y = 5x - 2
Use the table to answer the question.
x y
−5 0
0 5
2 7
Which linear equation represents this nonproportional linear relationship?
(1 point)
Responses
y=−x+5
y equals negative x plus 5
y=−5x+5
y equals negative 5 x plus 5
y=15x+5
y equals Start Fraction 1 over 5 End Fraction x plus 5
y=x+5
To determine the linear equation that represents the nonproportional linear relationship given in the table, we can calculate the slope by using the two points (0, 5) and (2, 7).
The formula for calculating the slope (m) when given two points (x₁, y₁) and (x₂, y₂) is:
m = (y₂ - y₁) / (x₂ - x₁)
Using the points (0, 5) and (2, 7):
m = (7 - 5) / (2 - 0)
m = 2 / 2
m = 1
So, we have a slope of 1. Now, we need to find the y-intercept (b) by substituting the slope and one of the points into the slope-intercept form equation y = mx + b.
Using the point (0, 5):
5 = 1(0) + b
5 = b
Therefore, the y-intercept (b) is 5.
The linear equation representing this nonproportional linear relationship is:
y = x + 5
So, the correct linear equation is:
y = x + 5
The table shows the number of parts, y, a machine produces each hour, x. Write an equation for this situation, and indicate if this is proportional or nonproportional.
y (number of parts) x (number of hours)
0 0
125 1
250 2
375 3
500 4(1 point)
Responses
y=125x+1, nonproportional
y equals 125 x plus 1 , nonproportional
y=x+125, nonproportional
y equals x plus 125 , nonproportional
y=125x, nonproportional
y equals 125 x , nonproportional
y=125x, proportional
To determine if the relationship between the number of parts produced by the machine each hour is proportional or nonproportional, let's look at the data in the table.
From the given data, we observe that the number of parts (y) is directly increasing in a linear manner with the number of hours (x). This means that for each hour, the machine produces an additional 125 parts.
When expressing this relationship in an equation form, it should be y = 125x. This equation correctly represents the situation, and it is proportional because as x increases, y increases by a constant ratio of 125.
Therefore, the correct equation is:
y = 125x, proportional.
Write y−6x=5 in slope-intercept form(1 point)
y=
To express the equation y - 6x = 5 in slope-intercept form (y = mx + b), we need to solve for y.
Starting with the given equation:
y - 6x = 5
Add 6x to both sides to isolate y:
y = 6x + 5
So, the equation y - 6x = 5 can be rewritten in slope-intercept form as:
y = 6x + 5
Graph the equation x−y=6 using the form y=mx+b.(1 point)
Responses
An illustration shows a coordinate plane with four quadrants. The x and y axes range from negative 10 to 10 in one unit increments. An upward slanting line is graphed on the coordinate plane. The upward slanting line passes through closed points plotted at left parenthesis 0 comma negative 6 right parenthesis and left parenthesis 1 comma negative 5 right parenthesis.
Image with alt text: An illustration shows a coordinate plane with four quadrants. The x and y axes range from negative 10 to 10 in one unit increments. An upward slanting line is graphed on the coordinate plane. The upward slanting line passes through closed points plotted at left parenthesis 0 comma negative 6 right parenthesis and left parenthesis 1 comma negative 5 right parenthesis.
A coordinate plane shows the x-axis ranging from negative 9 to 9 in increments of 1 and the y-axis ranging from 11 to negative 11 in increments of 1. A line with arrows at both ends joins two plotted points. The coordinates of the plotted points are as follows: left parenthesis 0 comma 3 right parenthesis, and left parenthesis 3 comma 2 right parenthesis.
Image with alt text: A coordinate plane shows the x-axis ranging from negative 9 to 9 in increments of 1 and the y-axis ranging from 11 to negative 11 in increments of 1. A line with arrows at both ends joins two plotted points. The coordinates of the plotted points are as follows: left parenthesis 0 comma 3 right parenthesis, and left parenthesis 3 comma 2 right parenthesis.
An illustration shows a coordinate plane with the x-axis ranging from negative 9 to 9 in one unit increments, and the y-axis ranging from negative 11 to 11 in one unit increments. A solid line passes through two plotted points and extends beyond. A solid line with arrows at both ends passes through points with coordinates left parenthesis 0 comma 0 right parenthesis and left parenthesis 6 comma 6 right parenthesis.
Image with alt text: An illustration shows a coordinate plane with the x-axis ranging from negative 9 to 9 in one unit increments, and the y-axis ranging from negative 11 to 11 in one unit increments. A solid line passes through two plotted points and extends beyond. A solid line with arrows at both ends passes through points with coordinates left parenthesis 0 comma 0 right parenthesis and left parenthesis 6 comma 6 right parenthesis.
A coordinate plane shows the x-axis ranging from negative 9 to 9 in increments of 1 and the y-axis ranging from 11 to negative 11 in increments of 1. A line with arrows at both ends joins two plotted points. The coordinates of the plotted points are as follows: left parenthesis 0 comma negative 4 right parenthesis, and left parenthesis 1 comma negative 10 right parenthesis.
Image with alt text: A coordinate plane shows the x-axis ranging from negative 9 to 9 in increments of 1 and the y-axis ranging from 11 to negative 11 in increments of 1. A line with arrows at both ends joins two plotted points. The coordinates of the plotted points are as follows: left parenthesis 0 comma negative 4 right parenthesis, and left parenthesis 1 comma negative 10 right parenthesis.