Question

2 the graph shows the amounts of almonds, in grams, for different amounts of oats, in cups, in a granola mix. label the point $(1,k)$ on the graph, find the value of $k$, and explain its meaning.

Explanation:

Step1: Determine the value of \(k\)

Since the graph is a straight - line passing through the origin, it represents a proportional relationship. We can use the unit - rate concept.
If we assume two points \((x_1,y_1)=(2,50)\) (from the graph, when \(x = 2\) cups of oats, \(y = 50\) grams of almonds). The equation of a proportional relationship is \(y=mx\), where \(m\) is the slope (unit rate).
The slope \(m=\frac{y_1}{x_1}\). Substituting \(x_1 = 2\) and \(y_1=50\), we get \(m=\frac{50}{2}=25\).
When \(x = 1\) (for the point \((1,k)\)), using the equation \(y=mx\) (where \(m = 25\)), we have \(k=25\times1\).

Step2: Explain the meaning of \(k\)

In the context of the problem, \(k\) represents the number of grams of almonds per cup of oats.

Answer:

\(k = 25\). The value of \(k\) means that there are 25 grams of almonds per cup of oats in the granola mix.