Let's go through the questions based on the trend line equation provided, $Y = 1.17x - 0.94$:

Solution to Each Question

A. What is the equation of the current trend line in the Gizmo?

• The equation given is $Y = 1.17x - 0.94$.

B. Turn on Show probe. Drag the probe to $x = 0$. What is the value of $y$?

• When $x = 0$, substitute into the equation: $Y = 1.17(0) - 0.94 = -0.94$
• So, $y = -0.94$.

C. What part of the trend line equation is equal to this value?

• This value, $-0.94$, is the y-intercept of the trend line. It represents the value of $y$ when $x = 0$.

D. Carefully drag the probe to $x = 1$. What is the value of $y$?

• When $x = 1$, substitute into the equation: $Y = 1.17(1) - 0.94 = 1.17 - 0.94 = 0.23$
• So, $y = 0.23$.

E. How much did the value of $y$ increase from $x = 0$ to $x = 1$?

• The increase in $y$ is the difference between the values at $x = 1$ and $x = 0$: $0.23 - (-0.94) = 0.23 + 0.94 = 1.17$
• So, $y$ increased by $1.17$.

F. What part of the equation is equal to this value?

• This value, $1.17$, is the slope of the line. It represents the amount that $y$ changes for each unit increase in $x$.

Would you like further clarification or have additional questions?

Here are five related questions to expand your understanding:

1. How do you interpret the slope in a real-world context?
2. What does a negative y-intercept imply about the trend line?
3. If the slope were negative, how would that affect the graph of the line?
4. How could you determine the x-intercept of the trend line from the equation?
5. How does changing the y-intercept value affect the position of the line on the graph?

Tip: Remember, the slope indicates the "steepness" of the line, showing how much $y$ changes as $x$ increases by 1 unit.