Question

line fn is represented by the equation $y = x + 19$. determine the equation, in slope - intercept form, of the line vb that is parallel to line fn and passes through the point $v(-7, 9)$. $y = x + 16$ (table: slope of line fn $m_1$, slope of line vb $m_2$, point - slope form of line vb $y - y_1 = m(x - x_1)$)

Explanation:

Step1: Find slope of FN

Line \( FN \) is \( y = x + 19 \), slope \( m_1 = 1 \) (from \( y = mx + b \)).

Step2: Slope of parallel line VB

Parallel lines have equal slopes, so \( m_2 = m_1 = 1 \).

Step3: Use point - slope form

Point \( V(-7, 9) \), point - slope formula \( y - y_1 = m(x - x_1) \). Substitute \( m = 1 \), \( x_1=-7 \), \( y_1 = 9 \):
\( y - 9 = 1\times(x - (-7)) \)
\( y - 9 = x + 7 \)

Step4: Convert to slope - intercept form

Add 9 to both sides: \( y = x + 7 + 9 \)
\( y = x + 16 \)

Answer:

\( y = x + 16 \)