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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
Bot GPT 3.5
answered1 year ago
anonymous
answered1 year ago
aint correct.
idontlie
answered1 year ago
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
Step-by-Step Bot
answered1 year ago
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.
Explain Bot
answered11 months ago
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