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To solve this problem, we are asked to write the equation of a line in slope-intercept form, which is typically given as:

\[
y = mx + b
\]

Where:
- \( m \) is the slope of the line, and
- \( b \) is the y-intercept.

### Given information:
- x-intercept = \((-6, 0)\)
- y-intercept = \((0, 5)\)

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

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

Substituting the given intercept points:
- \((x_1, y_1) = (-6, 0)\)
- \((x_2, y_2) = (0, 5)\)

\[
m = \frac{5 - 0}{0 - (-6)} = \frac{5}{6}
\]

#### Step 2: Write the equation
Now that we have the slope \(m = \frac{5}{6}\) and the y-intercept \(b = 5\), we can write the equation of the line in slope-intercept form:

\[
y = \frac{5}{6}x + 5
\]

This is the equation of the line. Would you like a more detailed breakdown, or do you have any questions?

### Related Questions:
1. What is the equation of a line if the x-intercept is \((4, 0)\) and the y-intercept is \((0, 7)\)?
2. How does the slope affect the angle of a line with respect to the x-axis?
3. Can you find the equation of a line passing through points \((1, 2)\) and \((4, 6)\)?
4. What is the equation of a vertical line that passes through the point \((-6, 5)\)?
5. How would you write the equation if the slope is negative and the intercept is \((0, -3)\)?

### Tip:
Remember, the slope \(m\) tells you how much the line rises or falls for each unit increase in \(x\). The y-intercept \(b\) is where the line crosses the y-axis.

Write an equation in slope-intercept form for the line described. x-intercept (-6, 0), y-intercept (0, 5).

Learn how to write the equation of a line in slope-intercept form when given the x-intercept (-6, 0) and y-intercept (0, 5). This problem involves finding the slope and constructing the equation using the formula y = mx + b. Suitable for Grades 7-9 students.

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