Use the given conditions to write an equation for the line in point-slope form and in slope-intercept form. Passing through (3, 6) with x-intercept -3

To find the equation of a line, we need two things: a point on the line and the slope. You have one point \((3, 6)\) and an \(x\)-intercept of \(-3\). Let's break this down step-by-step:

### Step 1: Find the slope (\(m\))
The \(x\)-intercept is \((-3, 0)\), which is another point on the line. Using the two points \((3, 6)\) and \((-3, 0)\), we can find the slope.

The slope formula is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substitute \((x_1, y_1) = (3, 6)\) and \((x_2, y_2) = (-3, 0)\):
\[
m = \frac{0 - 6}{-3 - 3} = \frac{-6}{-6} = 1
\]
So, the slope \(m = 1\).

### Step 2: Write the equation in **point-slope form**
The point-slope form of a line is:
\[
y - y_1 = m(x - x_1)
\]
Substitute \(m = 1\) and \((x_1, y_1) = (3, 6)\):
\[
y - 6 = 1(x - 3)
\]
Simplifying:
\[
y - 6 = x - 3
\]
This is the **point-slope form** of the equation.

### Step 3: Convert to **slope-intercept form**
The slope-intercept form is:
\[
y = mx + b
\]
We already know that \(m = 1\). Let's simplify the point-slope form equation to slope-intercept form:
\[
y - 6 = x - 3
\]
Add 6 to both sides:
\[
y = x + 3
\]
So, the **slope-intercept form** of the equation is:
\[
y = x + 3
\]

### Final Answer:
- **Point-slope form**: \( y - 6 = x - 3 \)
- **Slope-intercept form**: \( y = x + 3 \)

Would you like any more details or have any questions?

Here are 5 related questions to explore:
1. How do you find the slope between any two points?
2. What is the general form of a linear equation?
3. How do you convert from slope-intercept form to standard form?
4. What does the x-intercept of a line represent geometrically?
5. Can a line have more than one x-intercept?

**Tip:** The point-slope form is especially useful when you know a point on the line and the slope.

Use the given conditions to write an equation for the line in point-slope form and in slope-intercept form. Passing through (3, 6) with x-intercept -3.

Learn how to find the equation of a line passing through the point (3, 6) with an x-intercept of -3. This problem involves key algebraic concepts such as the slope formula, point-slope form, and slope-intercept form. Ideal for students in Grades 8-10.

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