Question

points on a graph: (0,0) (1,12) (2,24) (3,36)
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 determine the equation of the line through the origin given the points on the graph, we can observe the relationship between the \(x\) and \(y\) values.

The provided points on the graph are:
- (0, 0)
- (1, 12)
- (2, 24)
- (3, 36)

From these points, we can see the pattern in the \(y\) values as we increase \(x\):

- When \(x = 1\), \(y = 12\)
- When \(x = 2\), \(y = 24\)
- When \(x = 3\), \(y = 36\)

Notice that for every increase of \(1\) in \(x\), \(y\) increases by \(12\). Thus, the relationship between \(y\) and \(x\) can be expressed in a linear form:

\[
y = mx
\]

where \(m\) is the slope. The slope \(m\) can be determined from the relationship:

\[
m = \frac{\Delta y}{\Delta x} = \frac{12}{1} = 12
\]

Putting this into the linear equation, we get:

\[
y = 12x
\]

Thus, the equation of the line through the origin is:

**y = 12x**

The correct response from the options provided is:

**y = 12x**