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To find the formula for the linear function \( h(x) \) given that \( h(-30) = -80 \) and \( h(40) = 60 \), we can use the information provided to determine the slope and then find the equation in slope-intercept form.

### Step 1: Find the slope \( m \)
The slope \( m \) of a line through two points \((x_1, y_1)\) and \((x_2, y_2)\) is calculated as:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points \((-30, -80)\) and \( (40, 60) \):

\[
m = \frac{60 - (-80)}{40 - (-30)} = \frac{60 + 80}{40 + 30} = \frac{140}{70} = 2
\]

### Step 2: Use the slope and one point to find the y-intercept \( b \)
The slope-intercept form of the equation is:
\[
h(x) = mx + b
\]
Using the slope \( m = 2 \) and the point \( (-30, -80) \):

\[
-80 = 2(-30) + b
\]
\[
-80 = -60 + b
\]
\[
b = -80 + 60 = -20
\]

### Final equation:
The equation of the linear function is:
\[
h(x) = 2x - 20
\]

Would you like any further details or explanations on this?

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Here are 5 related questions for further practice:
1. What is the slope of the line that passes through the points \( (2, 3) \) and \( (4, 7) \)?
2. How do you interpret the slope of a line in a real-world context?
3. Can you find the equation of a line parallel to \( h(x) = 2x - 20 \) that passes through the point \( (0, 5) \)?
4. What is the y-intercept of the line \( h(x) = 2x - 20 \)?
5. How would the graph of \( h(x) = 2x - 20 \) change if the slope were negative?

**Tip:** Always double-check your calculations, especially when finding the slope, to ensure the accuracy of your linear equations.

Find a possible formula for the linear function h(x) if h(-30) = -80 and h(40) = 60. Write the equation in slope-intercept form.

Learn how to find the linear function equation given two points: h(-30) = -80 and h(40) = 60. This problem involves calculating the slope and using it to determine the equation in slope-intercept form. Suitable for students in Grades 8-10.

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