Question

line rv is perpendicular to line ac. line ac is represented by the equation $y = \frac{3}{2}x + 5$. line rv passes through the point r (0, 3). determine the equation of line rv in slope - intercept form. $y = \square$

Explanation:

Step1: Find slope of AC

The equation of line \( AC \) is \( y = \frac{3}{2}x + 5 \). The slope of \( AC \), \( m_{AC} = \frac{3}{2} \).

Step2: Find slope of RV (perpendicular)

For perpendicular lines, the product of slopes is -1. Let \( m_{RV} \) be the slope of \( RV \). Then \( m_{AC} \times m_{RV} = -1 \). So \( \frac{3}{2} \times m_{RV} = -1 \), which gives \( m_{RV} = -\frac{2}{3} \).

Step3: Use point - slope form for RV

Line \( RV \) passes through \( R(0, 3) \). The slope - intercept form is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. Since the line passes through \( (0, 3) \), the y - intercept \( b = 3 \), and \( m = -\frac{2}{3} \). So the equation of line \( RV \) is \( y=-\frac{2}{3}x + 3 \).

Answer:

\( y = -\frac{2}{3}x + 3 \)