Question

Write the​ point-slope form of the line satisfying the given conditions. Then use the​ point-slope form of the equation to write the​ slope-intercept form of the equation.
Slopeequals8​, passing through ​(negative 6​,1​)
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Part 1
Type the​ point-slope form of the equation of the line.
  
enter your response here
​(Simplify your answer. Use integers or fractions for any numbers in the​ equation.)

Answer 1

To write the point-slope form of the equation of a line, we can use the formula:

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

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

Given:
- Slope \( m = 8 \)
- Point \((x_1, y_1) = (-6, 1)\)

Plugging in these values:

\[
y - 1 = 8(x - (-6))
\]

This simplifies to:

\[
y - 1 = 8(x + 6)
\]

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

\[
y - 1 = 8(x + 6)
\]

---

### Part 2: Convert to Slope-Intercept Form

To convert to slope-intercept form, we need to isolate \( y \):

Start with:

\[
y - 1 = 8(x + 6)
\]

Distribute the \( 8 \):

\[
y - 1 = 8x + 48
\]

Now, add \( 1 \) to both sides:

\[
y = 8x + 48 + 1
\]

\[
y = 8x + 49
\]

Thus, the slope-intercept form of the equation is:

\[
y = 8x + 49
\]

### Summary
1. **Point-Slope Form:** \( y - 1 = 8(x + 6) \)
2. **Slope-Intercept Form:** \( y = 8x + 49 \)