Question

lesson 3 - 3 exit ticket for items 1 and 2, use the graph to complete the exercises. 1. write the ratio of side lengths for each right triangle. 2. what are the slopes of the hypotenuses? how does this relate to the slope of the line? name date period lesson 3 - 4 exit ticket for items 1 and 2, use the graph showing the average distance max runs per hour to complete the exercises. 1. consider a right triangle whose hypotenuse lies on the line. complete the sentence. the ratio of the height of any right triangle drawn to the base of any right triangle is ____ to ____. 2. what is the equation of the line in the form y = mx for the graph?

Explanation:

1.

Step1: Select two points on the line

Let's take two points \((0,0)\) and \((1,5)\) from the graph of the running - distance vs time.

Step2: Calculate the ratio of height to base

The height (change in \(y\)) and base (change in \(x\)) for a right - triangle with hypotenuse on the line. The ratio of the height of the right - triangle to the base is the slope. For the points \((0,0)\) and \((1,5)\), the change in \(y\) is \(5 - 0=5\) and the change in \(x\) is \(1 - 0 = 1\). The ratio is \(5\) to \(1\).

Step1: Recall the slope - intercept form

The equation of a line is \(y=mx\), where \(m\) is the slope.

Step2: Determine the slope

We found the slope \(m\) in part 1. The slope \(m = 5\) (since the ratio of the height to the base of the right - triangle with hypotenuse on the line is \(5\) to \(1\)).

Answer:

5, 1
2.