Question

1. line j passes though the point (2, 0) and is perpendicular to the graph of $y = \frac{1}{4}x - 3$. line k is parallel to line j and passes through point (-1,6). what is the equation in slope - intercept from of line k?

Explanation:

Step1: Find slope of line \( j \)

The slope of \( y = \frac{1}{4}x - 3 \) is \( m_1=\frac{1}{4} \). For perpendicular lines, \( m_1 \cdot m_2=-1 \), so \( \frac{1}{4} \cdot m_2=-1 \), solving gives \( m_2 = - 4 \). Thus, slope of line \( j \) is \( -4 \).

Step2: Slope of line \( k \)

Since line \( k \) is parallel to line \( j \), their slopes are equal. So slope of line \( k \), \( m=-4 \).

Step3: Equation of line \( k \)

Using point - slope form \( y - y_1=m(x - x_1) \) with point \( (-1,6) \) and \( m = - 4 \):
\( y - 6=-4(x + 1) \)
Expand: \( y - 6=-4x-4 \)
Add 6 to both sides: \( y=-4x + 2 \)

Answer:

\( y=-4x + 2 \)