Graphing Proportional Relationships Quick Check
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Question
Use the image to answer the question.
An illustration shows a graph labeled Inches per Feet. The horizontal axis is labeled feet and ranges from 0 to 4 in increments of 1. The vertical axis is labeled Inches and ranges from 0 to 40 in increments of 4. An upward slanting line segment connects points plotted at left parenthesis 0 comma 0 right parenthesis, left parenthesis 1 comma 12 right parenthesis, left parenthesis 2 comma 24 right parenthesis, and left parenthesis 3 comma 36 right parenthesis.
The proportional relationship between inches and feet is displayed on the graph. Derive the equation of the line through the origin.
(1 point)
Responses
y=112x
y equals Start Fraction 1 over 12 End Fraction x
y=12x
y equals 12 x
y=36x
y equals 36 x
y=2x
1:(1/4, 1
2: 1,30
3:Yes, the data table has a proportional relationship
4:No, not all of the ratios are proportional or have equivalence.
5:Yes, the ratios are in a proportional relationship.
trust me if u want
y=12x
aint correct.
To derive the equation of the line through the origin, we can observe that the line passes through the point (0,0). The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.
Since the line passes through the origin, the y-intercept (b) is 0.
To find the slope (m), we can choose any two points on the line and calculate the change in y divided by the change in x. Let's take the points (0,0) and (1,12) from the graph.
Using these points, we have:
Change in y = 12 - 0 = 12
Change in x = 1 - 0 = 1
Therefore, the slope (m) is 12/1 = 12.
Since the equation is y = mx + b and b = 0, the equation of the line through the origin is:
y = 12x.
So, the correct answer is:
y = 12x.
To derive the equation of the line through the origin on the given graph, we need to determine the slope of the line. The slope represents how much the y-coordinate (inches) changes for every unit increase in the x-coordinate (feet).
Looking at the graph, we can see that for every increase of 1 foot, the inches increase by 12. This means that the slope of the line is 12.
Since the line passes through the origin (0,0), we can use the slope-intercept form of a linear equation to find the equation of the line. The slope-intercept form is y = mx + b, where m represents the slope and b represents the y-intercept.
In this case, the equation would be y = 12x + 0. However, since the y-intercept is 0, we can simply write the equation as y = 12x.
Therefore, the equation of the line through the origin is y = 12x.
So the correct answer is:
y = 12x