A line has a slope of 7 and passes through the point (
–
1,
–
8). Write its equation in slope-intercept form.

To find the equation of a line in slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept, we can use the given slope and the point it passes through.

1. **Given**: 
   - Slope (\( m \)) = 7
   - Point = \( (-1, -8) \)

2. **Using the point-slope form of the equation**:
   \[
   y - y_1 = m(x - x_1)
   \]
   Substituting the values:
   \[
   y - (-8) = 7(x - (-1))
   \]
   This simplifies to:
   \[
   y + 8 = 7(x + 1)
   \]

3. **Distributing**:
   \[
   y + 8 = 7x + 7
   \]

4. **Solving for \( y \)**:
   \[
   y = 7x + 7 - 8
   \]
   \[
   y = 7x - 1
   \]

Thus, the equation of the line in slope-intercept form is:
\[
y = 7x - 1
\]

### Would you like any further details or have any questions?

Here are some related questions you might consider:
1. How do you find the y-intercept from a given equation?
2. What is the relationship between slope and parallel lines?
3. How would the equation change if the slope were negative?
4. Can you convert this equation into standard form?
5. What is the significance of the slope in real-world applications?

**Tip**: When given a point and a slope, always start with the point-slope form for easy calculations!

A line has a slope of 7 and passes through the point (-1, -8). Write its equation in slope-intercept form.

Discover how to derive the equation of a line with a slope of 7 passing through the point (-1, -8) in slope-intercept form. This step-by-step solution covers essential algebraic concepts and formulas. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation