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To write the equation of the line that passes through the points \((0, 4)\) and \((6, 0)\) in standard form, we follow these steps:

### Step 1: Find the slope of the line
The formula for the slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substituting the points \((0, 4)\) and \((6, 0)\):
\[
m = \frac{0 - 4}{6 - 0} = \frac{-4}{6} = -\frac{2}{3}
\]

### Step 2: Use the point-slope form of the line equation
The point-slope form of the line equation is:
\[
y - y_1 = m(x - x_1)
\]
Using the point \((0, 4)\) and the slope \(m = -\frac{2}{3}\):
\[
y - 4 = -\frac{2}{3}(x - 0)
\]
Simplifying this:
\[
y - 4 = -\frac{2}{3}x
\]
\[
y = -\frac{2}{3}x + 4
\]

### Step 3: Convert to standard form
The standard form of a line is \(Ax + By = C\), where \(A\), \(B\), and \(C\) are integers.

Starting from:
\[
y = -\frac{2}{3}x + 4
\]
Multiply through by 3 to eliminate the fraction:
\[
3y = -2x + 12
\]
Rearranging to standard form:
\[
2x + 3y = 12
\]

Thus, the equation of the line in standard form is:
\[
2x + 3y = 12
\]

Would you like further clarification, or do you have any questions? Here are 5 related questions for practice:

1. What is the standard form equation of a line passing through \((2, 3)\) and \((4, -1)\)?
2. How do you find the slope between two points?
3. How do you convert the equation \(y = mx + b\) to standard form?
4. What are the differences between point-slope form and standard form?
5. How do you find the equation of a vertical line?

**Tip:** Always check if the slope simplifies when finding the slope between two points!

Write an equation in standard form for the line that passes through the given points (0,4) and (6,0).

Learn how to write the equation of a line in standard form that passes through the points (0,4) and (6,0). This problem covers key concepts of linear equations and coordinate geometry. Suitable for Grade 8 students.

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