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The problem asks to write the equation of a line in standard form that passes through the points \((0, 4)\) and \((6, 0)\).

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

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

Substitute the given 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
The point-slope form of a line is:

\[
y - y_1 = m(x - x_1)
\]

Using the slope \(m = -\frac{2}{3}\) and one of the points, say \((0, 4)\):

\[
y - 4 = -\frac{2}{3}(x - 0)
\]

Simplify:

\[
y - 4 = -\frac{2}{3}x
\]

\[
y = -\frac{2}{3}x + 4
\]

### Step 3: Convert to standard form
The standard form of a line is:

\[
Ax + By = C
\]

We need to eliminate the fraction. Multiply the entire equation by 3:

\[
3y = -2x + 12
\]

Now move the \(x\)-term to the left-hand side to get it in standard form:

\[
2x + 3y = 12
\]

Thus, the equation of the line in standard form is:

\[
2x + 3y = 12
\]

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:
1. How do you find the slope of a line given two points?
2. What is the significance of the standard form of a linear equation?
3. How would the equation change if the points were different?
4. Can you rewrite the equation of a line in slope-intercept form?
5. What are the key differences between slope-intercept form and standard form?

**Tip:** When converting a line equation to standard form, try to eliminate fractions by multiplying through by the least common denominator (LCD).

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 involves finding the slope and converting from point-slope form to standard form. Perfect for students in Grades 8-10.

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