write an equation of the line that passes through the points x-intercept:(2,0) y intercept:(0,3)

To write the equation of a line passing through two points, we need to determine the slope and then use the slope-intercept form of a line, which is:

\[
y = mx + b
\]

where:
- \( m \) is the slope of the line
- \( b \) is the y-intercept

### Step 1: Find the Slope (m)

Given the two points:
- \( x \)-intercept: \( (2, 0) \)
- \( y \)-intercept: \( (0, 3) \)

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

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

Substitute the points \((x_1, y_1) = (2, 0)\) and \((x_2, y_2) = (0, 3)\):

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

### Step 2: Use the Slope-Intercept Form

We already have the y-intercept \(b = 3\), so we can substitute \(m = -\frac{3}{2}\) and \(b = 3\) into the slope-intercept form:

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

### Final Equation

The equation of the line that passes through the points \((2, 0)\) and \((0, 3)\) is:

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

Would you like further details or have any questions?

### Related Questions:
1. How do you convert the equation of a line from slope-intercept form to standard form?
2. What is the point-slope form of the equation of a line, and how can it be derived from two points?
3. How can you find the distance between the two intercepts?
4. How do you determine if two lines are parallel or perpendicular?
5. What is the effect on the slope of a line if you switch the x- and y-intercepts?

**Tip:** Remember that the slope represents the rate of change or steepness of a line. The greater the absolute value of the slope, the steeper the line.

Learn how to write the equation of a line passing through the x-intercept (2,0) and y-intercept (0,3) using the slope formula and slope-intercept form. This problem covers key concepts in coordinate geometry and linear equations. Suitable for students in Grades 7-9.

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