Question

the graph shows the cost, y, in dollars for a given number of pounds of yuca, x, that matias buys from the supermarket. what do the triangles tell you about the slope? complete each statement. the triangles are? the ratios of the corresponding side lengths are? the slope of each part of the line is?

Explanation:

Step1: Determine the relationship between the triangles

The triangles formed by the line on the graph are similar. This is because the angles of the triangles are equal (corresponding angles as the line has a constant slope).

Step2: Analyze the ratios of corresponding side lengths

For similar triangles, the ratios of the corresponding side lengths are equal. This is a property of similar triangles.

Step3: Calculate the slope

The slope \(m\) of a line is given by the formula \(m=\frac{\text{rise}}{\text{run}}\). For example, if we consider the triangle from \((0,0)\) to \((2,3)\) (assuming coordinates based on the graph - let's say \(E=(2,0)\), \(B=(2,3)\)), \(\text{rise}=3\), \(\text{run} = 2\), \(m=\frac{3}{2}\). If we take another triangle (say from \((2,3)\) to \((4,6)\)), \(\text{rise}=6 - 3=3\), \(\text{run}=4 - 2 = 2\), \(m=\frac{3}{2}\). The slope of each part of the line is the same.

Answer:

The triangles are similar. The ratios of the corresponding side lengths are equal. The slope of each part of the line is the same.