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.