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.

Question

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

Answer 1

To derive the equation of the line represented in the graph, we need to identify the relationship between the input (feet) and output (inches).

From the points given:

• At 0 feet, 0 inches: $(0,0)$
• At 1 foot, 12 inches: $(1,12)$
• At 2 feet, 24 inches: $(2,24)$
• At 3 feet, 36 inches: $(3,36)$

We can observe that for every 1 foot increase, there is a corresponding increase of 12 inches. Therefore, the relationship can be described by the slope of the line, which is:

$$\text{slope}=\frac{\text{change in inches}}{\text{change in feet}}=\frac{12-0}{1-0}=12$$

Since the line passes through the origin (0,0), this confirms that the equation of the line in slope-intercept form $y=mx+b$ results in:

$$y=12x$$

Thus, the correct equation is:

y = 12x