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 $v(-7, 9)$. $y = \square$ \

slope of line fn	slope of line vb	point - slope form of line vb	\
----	----	----	\
$m_1$	$m_2$	$y - y_1 = m(x - x_1)$

Explanation:

Step1: Find slope of FN

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

Step2: Slope of VB (parallel)

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

Step3: Point - Slope Form

Using point \( V(-7, 9) \) and \( m = 1 \), point - slope form: \( y - 9 = 1(x - (-7)) \), simplifies to \( y - 9 = x + 7 \).

Step4: Slope - Intercept Form

Solve for \( y \): \( y = x + 7 + 9 \), so \( y = x + 16 \).

Answer:

\( y = x + 16 \)