Question

the following graph contains line s and point r. line s contains points (-3, 5) and (3,1). point r is located at (2, 6). state the slope of line s. -3/2 plot another point that lies on a line perpendicular to line s and passes through point r. (-2, 0) answer 1: -3/2 answer 2: (-2, 0)

Explanation:

Step1: Calculate slope of line s

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Given points $(-3,5)$ and $(3,1)$ on line s, we have $m_s=\frac{1 - 5}{3-(-3)}=\frac{-4}{6}=-\frac{2}{3}$.

Step2: Find slope of perpendicular line

If two lines are perpendicular, the product of their slopes is - 1. Let the slope of the perpendicular line be $m_p$. Then $m_s\times m_p=-1$. Substituting $m_s =-\frac{2}{3}$, we get $-\frac{2}{3}m_p=-1$, so $m_p=\frac{3}{2}$.

Step3: Use point - slope form to find another point

The point - slope form of a line is $y - y_1=m(x - x_1)$. We know the line passes through $R(2,6)$ with slope $m_p=\frac{3}{2}$. Let's find a new point. If we move 4 units to the left (change in $x$ is $\Delta x=-4$), then the change in $y$ is $\Delta y=m_p\times\Delta x=\frac{3}{2}\times(-4)=-6$. The new $x$ value is $x = 2-4=-2$ and the new $y$ value is $y=6 - 6 = 0$. So the point $(-2,0)$ lies on the perpendicular line.

Answer:

Slope of line s: $-\frac{2}{3}$
Another point on perpendicular line: $(-2,0)$