Question

line s has an equation of $y = 8x + 7$. line t is perpendicular to line s and passes through $(-8, -2)$. what is the equation of line t?
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 t

The slope of line \( s \) is \( 8 \). For perpendicular lines, the slope of line \( t \) (\( m_t \)) is the negative reciprocal of \( 8 \), so \( m_t = -\frac{1}{8} \).

Step2: Use point - slope form

The point - slope form is \( y - y_1 = m(x - x_1) \), where \( (x_1,y_1)=(-8,-2) \) and \( m = -\frac{1}{8} \). Substitute these values: \( y - (-2)=-\frac{1}{8}(x - (-8)) \), which simplifies to \( y + 2 = -\frac{1}{8}(x + 8) \).

Step3: Convert to slope - intercept form

Expand the right - hand side: \( y + 2 = -\frac{1}{8}x - 1 \). Subtract \( 2 \) from both sides: \( y=-\frac{1}{8}x - 1 - 2 \), so \( y = -\frac{1}{8}x - 3 \).

Answer:

\( y = -\frac{1}{8}x - 3 \)