Graphing Proportional Relationships Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
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Question
Use the image to answer the question.
An illustration shows a coordinate plane with 4 quadrants. The x-axis ranges from negative 9 to 9 in one unit increments, and the y-axis ranges from negative 11 to 11 in one unit increments. A line is graphed on the plane. An upward slanting line passes through points plotted at left parenthesis 1 comma 4 right parenthesis and left parenthesis 2 comma 8 right parenthesis.
Find the equation of the line y=mx through the origin that describes the proportional relationship shown in the graph.
(1 point)
To find the equation of the line y=mx through the origin, we need to find the slope (m) of the line.
The slope can be found using the formula:
m = (change in y) / (change in x)
From the given points (1,4) and (2,8), we can calculate the change in y and change in x:
Change in y = 8 - 4 = 4
Change in x = 2 - 1 = 1
Now, we can substitute these values into the slope formula:
m = 4 / 1 = 4
So, the equation of the line y=mx is y = 4x.
Compare Proportional Relationships Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
1 of 51 of 5 Items
Question
Use the table and image to answer the question.
Employee 1
Earnings per Hour
Hours Earnings
1 10
2 20
3 30
A line graph is titled as Employee 2, Earnings per Hour. The x-axis is labeled Hours ranging from 0 to 6 in increments of 1. The y-axis is labeled Earnings in dollars, ranging from 0 to 80 in increments of 5. A solid line joins four plotted points. The coordinates of the plotted points are as follows: 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.
The proportional relationship for the earnings and hours worked for Employee 1 is displayed in the table. The proportional relationship between the earnings and hours worked for Employee 2 is displayed in the graph. What is the equation that represents the proportional relationship between the earnings and hours worked for Employee 1 and Employee 2?
(1 point)
The equation for Employee 1 is
.
The equation for Employee 2 is
.
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To find the equation of the line y=mx through the origin that describes the proportional relationship shown in the graph, we need to find the slope (m) of the line.
The slope is calculated by taking the difference in y-coordinates and dividing it by the difference in x-coordinates of any two points on the line.
In this case, we have two points on the line which are: (1,4) and (2,8).
The difference in the y-coordinates is 8 - 4 = 4, and the difference in the x-coordinates is 2 - 1 = 1.
So, the slope (m) is 4/1 = 4.
Therefore, the equation of the line y=mx through the origin that describes the proportional relationship shown in the graph is y = 4x.
To find the equation of the line y = mx, where m represents the slope of the line, we need to determine the value of m.
In the given illustration, we can see that the line passes through the points (1, 4) and (2, 8). To find the slope, we can use the formula:
m = (change in y) / (change in x)
First, let's calculate the change in y:
change in y = y2 - y1 = 8 - 4 = 4
Next, let's calculate the change in x:
change in x = x2 - x1 = 2 - 1 = 1
Now, we can calculate the slope:
m = (change in y) / (change in x) = 4 / 1 = 4
So, the slope of the line is 4.
Now, we know that the equation of the line through the origin (0,0) with a slope of 4 is y = 4x.
Therefore, the equation of the line y=mx through the origin that describes the proportional relationship shown in the graph is y = 4x.