Given the following set of information, find a linear equation satisfying the conditions, if possible.

x-intercept at (–4, 0) and y-intercept at (0, –6)

To find the linear equation that satisfies the given conditions (x-intercept at \((-4, 0)\) and y-intercept at \((0, -6)\)), we can use the **slope-intercept form** of a line:

\[
y = mx + b
\]

### Step 1: Find the slope (m)
The slope of a line is calculated as:

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

Using the points \((-4, 0)\) and \((0, -6)\):

\[
m = \frac{-6 - 0}{0 - (-4)} = \frac{-6}{4} = -\frac{3}{2}
\]

### Step 2: Find the y-intercept (b)
From the given information, the y-intercept is \((0, -6)\), so \(b = -6\).

### Step 3: Write the equation
Now we can write the equation of the line by substituting the slope \(m = -\frac{3}{2}\) and the y-intercept \(b = -6\) into the slope-intercept form:

\[
y = -\frac{3}{2}x - 6
\]

### Final Answer:
The linear equation is:

\[
y = -\frac{3}{2}x - 6
\]

Would you like further details or have any questions?

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Here are five related questions:
1. How do you find the equation of a line given two points?
2. What is the significance of the slope in a linear equation?
3. How do you convert between slope-intercept form and standard form of a line?
4. How can you determine the slope of a vertical line?
5. How do you graph a line using its x- and y-intercepts?

**Tip:** When given intercepts, always start by finding the slope, then use either point to complete the equation.

Given the following set of information, find a linear equation satisfying the conditions, if possible. x-intercept at (–4, 0) and y-intercept at (0, –6)

Learn how to find the linear equation with x-intercept at (–4, 0) and y-intercept at (0, –6) using the slope-intercept form. This problem involves key algebraic concepts and is suitable for students in Grades 8-10.

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