Question

the equation for line t can be written as y = 4x - 8. line u, which is perpendicular to line t, includes the point (8, 8). what is the equation of line u? 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 u

The slope of line \( t \) is \( 4 \) (from \( y = 4x - 8 \), slope-intercept form \( y = mx + b \), where \( m \) is slope). For perpendicular lines, the product of slopes is \( -1 \). Let slope of \( u \) be \( m_u \). So \( 4 \times m_u = -1 \), then \( m_u = -\frac{1}{4} \).

Step2: Use point - slope form

Point - slope form is \( y - y_1 = m(x - x_1) \), where \( (x_1,y_1)=(8,8) \) and \( m = -\frac{1}{4} \). Substitute: \( y - 8 = -\frac{1}{4}(x - 8) \).

Step3: Convert to slope - intercept form

Expand the right - hand side: \( y - 8 = -\frac{1}{4}x + 2 \). Add 8 to both sides: \( y = -\frac{1}{4}x+2 + 8 \), so \( y = -\frac{1}{4}x + 10 \).

Answer:

\( y = -\frac{1}{4}x + 10 \)