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=12x
y equals 12 x
y=112x
y equals Start Fraction 1 over 12 End Fraction x
y=36x
y equals 36 x
y=2x
y equals 2 x
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The equation of the line through the origin is y = 12x.
To derive the equation of the line through the origin, we can use the slope-intercept form of a linear equation, which is y = mx, where m represents the slope of the line.
Looking at the graph, we can see that the line passes through the origin (0, 0) and the point (1, 12). We can use these two points to find the slope, m.
The formula for the slope between two points (x1, y1) and (x2, y2) is given by:
m = (y2 - y1) / (x2 - x1)
Using the coordinates (0, 0) and (1, 12) from the graph, we substitute the values into the formula:
m = (12 - 0) / (1 - 0)
m = 12/1
m = 12
Therefore, the slope of the line is 12.
Now, we can substitute the slope value into the slope-intercept form equation, y = mx, where m = 12:
y = 12x.
Hence, the equation of the line through the origin is y = 12x.