Question

2.5 hw part 3: perpendicular slope in slope-intercept form
for the equation of the line described below:
through (0, 4), perpendicular to $y = x - 5$
first, write the equation of the perpendicular line in point - slope form: $y\underline{\quad\quad}=\underline{\quad\quad}x\underline{\quad\quad}$
next, write the equation in slope - intercept form: $y = \underline{\quad\quad}x\underline{\quad\quad}$
(there are some number buttons: 1, -1, -0, +4, -4, +5, -5)

Explanation:

Step1: Find slope of perpendicular line

The slope of \( y = x - 5 \) is \( m_1 = 1 \). For perpendicular lines, \( m_1 \times m_2=-1 \), so \( m_2=-1 \).

Step2: Point - slope form

Point - slope form is \( y - y_1 = m(x - x_1) \). The point is \( (0,4) \), so \( x_1 = 0,y_1 = 4 \) and \( m=-1 \). Substituting, we get \( y - 4=-1(x - 0) \).

Step3: Slope - intercept form

Start with \( y - 4=-1(x - 0) \), simplify \( x - 0=x \), so \( y - 4=-x \). Then add 4 to both sides: \( y=-x + 4 \).

Answer:

• Point - slope form: \( y - 4=-1(x - 0) \)
• Slope - intercept form: \( y=-1x + 4 \)