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To write the equation of the line in slope-intercept form \( y = mx + b \), passing through the points \( (5, 4) \) and \( (-5, -10) \), we need to follow these steps:

### Step 1: Find the slope \( m \)
The formula for the slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Substitute the given points \( (5, 4) \) and \( (-5, -10) \):

\[
m = \frac{-10 - 4}{-5 - 5} = \frac{-14}{-10} = 1.4
\]

### Step 2: Use the slope-intercept form
Now that we have the slope \( m = 1.4 \), substitute this into the equation \( y = mx + b \).

### Step 3: Solve for the y-intercept \( b \)
Use one of the given points, say \( (5, 4) \), to solve for \( b \):

\[
4 = 1.4(5) + b
\]
\[
4 = 7 + b
\]
\[
b = 4 - 7 = -3
\]

### Final equation
Thus, the equation of the line is:

\[
y = 1.4x - 3
\]

Let me know if you need further details or explanations! Here are 5 related questions you might want to explore:

1. How would the equation change if the slope was negative?
2. What is the geometric interpretation of the y-intercept?
3. How can we rewrite the equation of the line in point-slope form?
4. How would you check if another point lies on the line?
5. What is the significance of parallel and perpendicular slopes?

**Tip**: When finding the equation of a line from two points, always calculate the slope first, as it defines the steepness and direction of the line.

Use your calculator to write the equation of a line in slope-intercept form that passes through the points (5, 4) and (-5, -10).

Learn how to write the equation of a line in slope-intercept form that passes through the points (5, 4) and (-5, -10). This problem explores key concepts such as the slope formula and linear equations, suitable for students in Grades 8-10.

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