Write an equation in point slope form of a line With an x intercept of (2,0) and a y intercept of (0,3)

To write the equation of a line in point-slope form, we need a point on the line and the slope.

### Step 1: Find the slope \( m \).
The slope \( m \) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

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

Using the points \((2, 0)\) (x-intercept) and \((0, 3)\) (y-intercept):

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

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

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

You can choose either \((2, 0)\) or \((0, 3)\) as the point \((x_1, y_1)\). Using \((2, 0)\):

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

This simplifies to:

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

So, the equation of the line in point-slope form is:

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

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:
1. How would the equation change if the line had a positive slope?
2. What is the equation of the line in slope-intercept form?
3. Can you find the distance between the x-intercept and y-intercept?
4. How do you convert the equation from point-slope to standard form?
5. What does the slope of \(-\frac{3}{2}\) indicate about the direction of the line?

**Tip:** When working with different forms of a line's equation, remember that converting between them often involves simple algebraic manipulations!

Learn how to write the equation of a line in point-slope form using intercepts (2,0) and (0,3). Step-by-step solution provided, including finding the slope and using the point-slope formula. Suitable for Grades 7-9.

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