Question

1. write the equation of the line that is perpendicular to y = 2x - 9 and passes through the point (-8, 0).

Explanation:

Step1: Find slope of perpendicular line

The given line is \( y = 2x - 9 \), so its slope (\( m_1 \)) is 2. For perpendicular lines, the product of slopes is -1 (\( m_1 \times m_2=-1 \)). Let \( m_2 \) be the slope of the required line. Then \( 2\times m_2=-1 \), so \( m_2 = -\frac{1}{2} \).

Step2: Use point - slope form

The point - slope form of a line is \( y - y_1=m(x - x_1) \), where \( (x_1,y_1)=(-8,0) \) and \( m = -\frac{1}{2} \). Substitute these values: \( y - 0=-\frac{1}{2}(x - (-8)) \).

Step3: Simplify the equation

Simplify \( y=-\frac{1}{2}(x + 8) \) to slope - intercept form. Distribute \( -\frac{1}{2} \): \( y=-\frac{1}{2}x-4 \).

Answer:

The equation of the line is \( y = -\frac{1}{2}x - 4 \)