Question

the equation of line ( c ) is ( y = -\frac{1}{8}x - 10 ). line ( d ) includes the point ( (-8, -5) ) and is parallel to line ( c ). what is the equation of line ( d )?
write the equation in slope - intercept form. write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

Explanation:

Step1: Find slope of line \( l \)

The equation of line \( l \) is \( y = -\frac{1}{8}x - 10 \). The slope of line \( l \), \( m_l \), is \( -\frac{1}{8} \). Since line \( k \) is perpendicular to line \( l \), the slope of line \( k \), \( m_k \), is the negative reciprocal of \( m_l \). So \( m_k = -\frac{1}{m_l} = -\frac{1}{-\frac{1}{8}} = 8 \).

Step2: Use point - slope form to find equation of line \( k \)

The point - slope form of a line is \( y - y_1 = m(x - x_1) \), where \( (x_1,y_1)=(-8,-5) \) and \( m = 8 \). Substitute these values into the formula:
\( y - (-5)=8(x - (-8)) \)
Simplify the equation:
\( y + 5 = 8(x + 8) \)
Expand the right - hand side:
\( y+5 = 8x+64 \)
Subtract 5 from both sides to get the slope - intercept form:
\( y = 8x+64 - 5 \)
\( y = 8x + 59 \)

Answer:

The equation of line \( k \) is \( y = 8x+59 \)