Write an equation in standard form for the line that passes through the given points.

left parenthesis 3 comma 0 right parenthesis(3,0) 

and left parenthesis 0 comma 2 right parenthesis(0,2)

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Part 1

The equation of the line in standard form is 

enter your response here

To find the equation of the line passing through the points \((3, 0)\) and \((0, 2)\), we follow these steps:

### 1. Find the slope of the line:
The slope \(m\) is given by the formula:

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

Substituting the coordinates \((x_1, y_1) = (3, 0)\) and \((x_2, y_2) = (0, 2)\):

\[
m = \frac{2 - 0}{0 - 3} = \frac{2}{-3} = -\frac{2}{3}
\]

### 2. Use the point-slope form of the equation:
The point-slope form of a line is:

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

Using the point \((3, 0)\) and the slope \(m = -\frac{2}{3}\):

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

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

### 3. Simplify the equation:
Distribute the slope:

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

### 4. Convert to standard form:
To convert to standard form \(Ax + By = C\), eliminate the fraction by multiplying the entire equation by 3:

\[
3y = -2x + 6
\]

Rearrange terms to get the standard form:

\[
2x + 3y = 6
\]

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

\[
\boxed{2x + 3y = 6}
\]

Would you like any further details or explanations?

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Here are 5 related questions to explore:

1. What is the slope-intercept form of a line?
2. How do you find the slope given two points?
3. What is the meaning of the slope in real-world applications?
4. Can a vertical line be expressed in standard form?
5. How do you convert from point-slope form to slope-intercept form?

**Tip:** The standard form of a linear equation is useful when you need to find intercepts quickly.

Write an equation in standard form for the line that passes through the points (3,0) and (0,2).

Learn how to write the equation of a line in standard form that passes through the points (3,0) and (0,2). This problem involves calculating the slope, using point-slope form, and converting to standard form. Suitable for students in Grades 8-10.

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