Y=9.0+0.5x is the data. What is the change in y for one unit change in x? What point does the line cross the y axis. What is the value of y when x=10.5

### 1. **Change in \( y \) for one unit change in \( x \):**

The equation \( y = 9.0 + 0.5x \) is in slope-intercept form \( y = mx + b \), where \( m \) is the slope. The slope \( m = 0.5 \) represents the change in \( y \) for every unit increase in \( x \). 

Thus, for every 1 unit increase in \( x \), \( y \) increases by **0.5**.

### 2. **Point where the line crosses the \( y \)-axis:**

To find where the line crosses the \( y \)-axis, set \( x = 0 \) in the equation \( y = 9.0 + 0.5x \).

\[
y = 9.0 + 0.5(0) = 9.0
\]

Therefore, the line crosses the \( y \)-axis at the point **(0, 9.0)**.

### 3. **Value of \( y \) when \( x = 10.5 \):**

Substitute \( x = 10.5 \) into the equation \( y = 9.0 + 0.5x \).

\[
y = 9.0 + 0.5(10.5) = 9.0 + 5.25 = 14.25
\]

Thus, when \( x = 10.5 \), the value of \( y \) is **14.25**.

Would you like any further details or have any questions?

### Follow-up Questions:
1. What is the interpretation of the slope \( 0.5 \) in a real-world scenario?
2. How do you find the slope if the equation is not given in slope-intercept form?
3. What happens to the line if we change the slope from \( 0.5 \) to a larger value?
4. Can we derive an equation from a given slope and y-intercept without the original equation?
5. How does the equation change if we modify the y-intercept?

### Tip:
The y-intercept in an equation represents the value of \( y \) when \( x = 0 \), and the slope indicates the rate of change of \( y \) with respect to \( x \).

Y = 9.0 + 0.5x is the data. What is the change in y for one unit change in x? What point does the line cross the y-axis? What is the value of y when x = 10.5?

Explore how to find the change in y for one unit change in x, the y-intercept, and the value of y when x = 10.5 for the linear equation Y = 9.0 + 0.5x. This problem covers key algebraic concepts suitable for students in Grades 6-8.

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