You are asked to find an equation of a line and are given the slope and a point on the line

instead of the slope and y-intercept. What would you do differently?

When given the slope and a point on the line, instead of the slope and y-intercept, the process of finding the equation of the line involves using the **point-slope form** of a linear equation. Here's how you would proceed:

### 1. **Recall the Point-Slope Form:**
The point-slope form of a linear equation is given by:

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

where:
- \( m \) is the slope of the line,
- \( (x_1, y_1) \) is a point on the line.

### 2. **Substitute the Given Values:**
- Substitute the given slope \( m \) into the equation.
- Substitute the coordinates of the given point \( (x_1, y_1) \) into the equation.

### 3. **Simplify the Equation:**
- After substituting, simplify the equation to put it in either the **slope-intercept form** \( y = mx + b \) or the **standard form** \( Ax + By = C \), depending on the requirement.

### **Example:**
Let's say you're given the slope \( m = 3 \) and a point on the line \( (2, -5) \).

1. Start with the point-slope form:
   \[
   y - (-5) = 3(x - 2)
   \]
   Simplifying:
   \[
   y + 5 = 3x - 6
   \]

2. To put it in slope-intercept form, solve for \( y \):
   \[
   y = 3x - 6 - 5
   \]
   \[
   y = 3x - 11
   \]

So, the equation of the line is \( y = 3x - 11 \).

### Conclusion:
The key difference is that when you have the slope and a point, you use the point-slope form to first establish the equation, and then you can convert it into the slope-intercept form or any other desired form.

Would you like to explore any more details or have other questions?

Here are some related questions that might be helpful:
1. How do you convert an equation from point-slope form to standard form?
2. What is the significance of the point-slope form of a line?
3. How would you find the y-intercept after using the point-slope form?
4. Can you determine the equation of a line if only two points are given?
5. How would the equation change if the slope is zero?

**Tip:** Always double-check the point's coordinates and the slope when substituting them into the point-slope form to avoid any calculation errors.

Learn how to find the equation of a line when given the slope and a point using the point-slope form of a linear equation. Example included. Suitable for Grades 7-9 students learning about linear equations.

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