Determine whether the graphs of the two equations are perpendicular. $$ y=2 x-9 $$ $$ 3 y=5-x $$ Are the graphs of the given equations perpendicular? No Yes

Question

UpStudy AI · Accepted Answer

The graphs are not perpendicular. To determine if the graphs of the two equations are perpendicular, we need to find the slopes of both lines and check if the product of the slopes is $$-1$$. 1. **First equation:** $$ y = 2x - 9 $$ The slope $$ m_1 $$ of this line is $$ 2 $$. 2. **Second equation:** $$ 3y = 5 - x $$ First, we need to rewrite this equation in slope-intercept form (i.e., $$ y = mx + b $$): $$ y = \frac{5 - x}{3} $$ $$ y = -\frac{1}{3}x + \frac{5}{3} $$ The slope $$ m_2 $$ of this line is $$ -\frac{1}{3} $$. 3. **Check if the slopes are negative reciprocals:** We need to check if $$ m_1 \cdot m_2 = -1 $$: $$ m_1 \cdot m_2 = 2 \cdot \left(-\frac{1}{3}\right) = -\frac{2}{3} $$ Since $$-\frac{2}{3} \neq -1$$, the slopes are not negative reciprocals. Therefore, the graphs of the given equations are **not perpendicular**. The answer is **No**.

Determine whether the graphs of the two equations are perpendicular. \( y=2 x-9 \) \( 3 y=5-x \) Are the graphs of the given equations perpendicular? No Yes

UpStudy ThothAI Solution

Step-by-step Solution

Quick Answer

Determine whether the graphs of the two equations are perpendicular. \( y=2 x-9 \) \( 3 y=5-x \) Are the graphs of the given equations perpendicular? No Yes

UpStudy ThothAI Solution

Step-by-step Solution

Quick Answer

Related Questions