Question

find the equation of a line parallel to $y + 9 = x$ that passes through the point $(4, 5)$.
answer
$\circ$ $y + 5 = - (x + 4)$ $\circ$ $y - 5 = - (x - 4)$
$\circ$ $y + 5 = x + 4$ $\circ$ $y - 5 = x - 4$

Explanation:

Step1: Find slope of given line

Rewrite \( y + 9 = x \) as \( y = x - 9 \). The slope (\(m\)) is \(1\) (since \(y = mx + b\), here \(m = 1\)). Parallel lines have the same slope, so the new line also has \(m = 1\).

Step2: Use point - slope form

Point - slope form is \( y - y_1 = m(x - x_1) \), where \((x_1,y_1)=(4,5)\) and \(m = 1\). Substituting, we get \( y - 5 = 1\times(x - 4) \), which simplifies to \( y - 5 = x - 4 \).

Answer:

D. \( y - 5 = x - 4 \) (assuming the last option is D, with the option text \( y - 5 = x - 4 \))