Use the image to answer the question.
An illustration shows two graphs depicting earnings per hour for employees 1 and 2. The first graph shows earnings per hour for employee 1. The horizontal axis shows hours ranging from 0 to 8 in increments of 2. The vertical axis shows earnings in dollars ranging from 0 to 80 in increments of 5. Four data points are plotted on the graph at left parenthesis 0 comma 0 right parenthesis, left parenthesis 2 comma 25 right parenthesis, left parenthesis 4 comma 50 right parenthesis, and left parenthesis 6 comma 75 right parenthesis. A line connects all the data points. The second graph shows earnings per hour for employee 2. The horizontal axis shows hours ranging from 0 to 6 in increments of 1. The vertical axis shows earnings in dollars ranging from 0 to 80 in increments of 5. Four data points are plotted on the graph at left parenthesis 0 comma 0 right parenthesis, left parenthesis 1 comma 15 right parenthesis, left parenthesis 3 comma 45 right parenthesis, and left parenthesis 5 comma 75 right parenthesis. A line connects all the data points.
The earnings for Employee 1 and Employee 2 are displayed in the following graphs. Which employee earns more per hour?
Employee 1 earns more per hour as their earnings increase at a faster rate compared to Employee 2. This can be observed by noticing the slope of the line connecting the data points for each employee on the graph.
Use the image to answer the question.
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 four 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, left parenthesis 1 comma 3 right parenthesis, left parenthesis 2 comma 6 right parenthesis, and left parenthesis 3 comma 9 right parenthesis. The solid line forms the hypotenuse for two triangles. The first triangle is marked with a dotted line and has vertices with coordinates left parenthesis 0 comma 0 right parenthesis, left parenthesis 1 comma 0 right parenthesis, and left parenthesis 1 comma 3 right parenthesis. The base is labeled as 1, and the perpendicular height on the right is labeled as 3. The second triangle is marked with a dashed line and has vertices with coordinates left parenthesis 1 comma 3 right parenthesis, left parenthesis 3 comma 3 right parenthesis, and left parenthesis 3 comma 9 right parenthesis. The base is labeled as 2, and the perpendicular height on the right is labeled as 6.
Use similar triangles to determine the slope of the line.
By using the similar triangles formed in the graph, we can determine the slope of the line by comparing the rise over the run for each triangle.
For the first triangle, the rise is 3 and the run is 1, giving us a slope of 3/1 = 3.
For the second triangle, the rise is 6 and the run is 2, giving us a slope of 6/2 = 3.
Since both similar triangles have the same slope of 3, we can conclude that the slope of the line passing through the points (0,0), (1,3), (2,6), and (3,9) is 3.
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.
To determine the cost per candy bar, we divide the cost by the quantity. Let's calculate the cost per bar for Candy Bar A using the data provided:
1. For 1 quantity, the cost per bar is 1.25
2. For 2 quantities, the cost per bar is 2.50 / 2 = 1.25
3. For 3 quantities, the cost per bar is 3.75 / 3 = 1.25
4. For 4 quantities, the cost per bar is 5.00 / 4 = 1.25
5. For 5 quantities, the cost per bar is 6.25 / 5 = 1.25
Therefore, the cost per candy bar for Candy Bar A is consistent at $1.25 per bar.
For Candy Bar B, the proportional relationship given is y=x, which means the cost per bar is equal to the quantity of bars.
Comparing the cost per bar for Candy Bar A and Candy Bar B, both have the same cost per bar of $1.25.
Therefore, Candy Bar A and Candy Bar B have the same cheapest cost per bar, which is $1.25. Enter 1 for Candy Bar A.
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.
To determine the equation of the line in slope-intercept form (y = mx + b), we first need to calculate the slope (m) of the line using the two points provided (0, -2) and (1, 3).
The formula to calculate the slope is:
m = (y2 - y1) / (x2 - x1)
Using the coordinates:
x1 = 0, y1 = -2
x2 = 1, y2 = 3
Substitute the values into the formula:
m = (3 - (-2)) / (1 - 0)
m = (3 + 2) / 1
m = 5
Now that we have the slope (m = 5), we can use the point-slope form of the equation to find the y-intercept (b). We can choose one of the points, let's use (0, -2):
y - y1 = m(x - x1)
y - (-2) = 5(x - 0)
y + 2 = 5x
Now, we can write this in slope-intercept form by isolating y:
y = 5x - 2
Therefore, the equation of the line in slope-intercept form is y = 5x - 2.
Graph the linear equation y=2x−3.
A. 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 downward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma negative 1 right parenthesis and left parenthesis 1 comma negative 3 right parenthesis.
B. 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 3 right parenthesis and left parenthesis 1 comma 5 right parenthesis.
C. 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 1 right parenthesis, and left parenthesis 1 comma 4 right parenthesis.
D. 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 1 comma negative 1 right parenthesis, and left parenthesis 0 comma negative 3 right parenthesis.
The correct option is:
B. An illustration of a coordinate plane with four quadrants shows the x-axis ranging from -9 to 9 and the y-axis ranging from -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 (0, 3) and (1, 5).
This matches the equation y = 2x - 3, where y = 3 when x = 0 and y = 5 when x = 1. The line is solid and upward, as expected for the equation y = 2x - 3.