Question

determine the equation for the trend line shown in each graph. move the correct answer to each box. not all answers will be used. ( y=\frac{9}{10}x ) ( y=\frac{10}{9}x ) ( y = 10x ) ( y=\frac{1}{10}x ) use ( (5,50) ) and ( (17,170) ) to find the slope. use ( (0,0) ) and ( (10,9) ) to find the slope.

Explanation:

Step1: Calculate the slope for the first graph

The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Using the points \((5,50)\) and \((17,170)\), we have \(m=\frac{170 - 50}{17 - 5}=\frac{120}{12}=10\). The equation of a line passing through the origin \((y = mx)\) is \(y = 10x\).

Step2: Calculate the slope for the second graph

Using the formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\) with points \((0,0)\) and \((10,9)\), we get \(m=\frac{9 - 0}{10 - 0}=\frac{9}{10}\). The equation of the line (since it passes through the origin \(y=mx\)) is \(y=\frac{9}{10}x\).

Answer:

For the first graph (using \((5,50)\) and \((17,170)\)): \(y = 10x\).
For the second graph (using \((0,0)\) and \((10,9)\)): \(y=\frac{9}{10}x\).