Question

the equation of line s is $y = -\frac{1}{9}x - 4$. line t includes the point (1, 7) and is perpendicular to line s. 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 \( -\frac{1}{9} \). For perpendicular lines, the slope of line \( t \) (\( m_t \)) is the negative reciprocal, so \( m_t = 9 \).

Step2: Use point - slope form

Point - slope form is \( y - y_1 = m(x - x_1) \), with \( (x_1,y_1)=(1,7) \) and \( m = 9 \). Substitute: \( y - 7 = 9(x - 1) \).

Step3: Convert to slope - intercept form

Expand: \( y - 7 = 9x - 9 \). Add 7 to both sides: \( y = 9x - 9 + 7 \), so \( y = 9x - 2 \).

Answer:

\( y = 9x - 2 \)