Question

the equation for line p is $y = 2x - 7$. line n is perpendicular to line p and passes through the point $(-4, 5)$. what is the y-intercept of line n?

Explanation:

Step1: Find slope of line n

The slope of line \( p \) is \( 2 \) (from \( y = 2x - 7 \)). For perpendicular lines, slopes are negative reciprocals. So slope of line \( n \), \( m = -\frac{1}{2} \).

Step2: Use point - slope form

Point - slope form is \( y - y_1 = m(x - x_1) \). Substitute \( m = -\frac{1}{2} \), \( x_1=-4 \), \( y_1 = 5 \):
\( y - 5=-\frac{1}{2}(x + 4) \)

Step3: Convert to slope - intercept form

Expand: \( y - 5=-\frac{1}{2}x - 2 \). Add 5 to both sides: \( y=-\frac{1}{2}x+3 \). The y - intercept is the constant term, which is 3.

Answer:

3