Question
Use the given conditions to write an equation for the line in point-slope form and slope-intercept form. Slope \( =-8 \), passing through \( (-6,-3) \) Type the point-slope form of the line. \( y+3=-8(x+6) \) (Simplify your answer. Use integers or fractions for any numbers in the equation.) Type the slope-intercept form of the line. \( \square \) (Simplify your answer. Use integers or fractions for any numbers in the equation.)
Ask by Osborne Howell. in the United States
Jan 25,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
Slope-intercept form: \( y = -8x - 51 \)
Solution
To convert the given point-slope form to slope-intercept form, follow these steps:
**Given:**
- Point-slope form: \( y + 3 = -8(x + 6) \)
**Steps to Convert to Slope-Intercept Form (\( y = mx + b \)):**
1. **Distribute the slope on the right side:**
\[
y + 3 = -8x - 48
\]
2. **Isolate \( y \) by subtracting 3 from both sides:**
\[
y = -8x - 48 - 3
\]
\[
y = -8x - 51
\]
**Slope-Intercept Form:**
\[
y = -8x - 51
\]
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Explain 
Simplify this solution Beyond the Answer
To convert your point-slope form into slope-intercept form, we start with the point-slope equation you've provided: 1. \( y + 3 = -8(x + 6) \) Now, let's expand and simplify to put it in slope-intercept form \( y = mx + b \): 2. Distributing the -8: \[ y + 3 = -8x - 48 \] 3. Now, subtract 3 from both sides: \[ y = -8x - 48 - 3 \] \[ y = -8x - 51 \] So, in slope-intercept form, the equation of the line is: \[ y = -8x - 51 \]
