Question

< 2 - 4 teacher_s_slope_parallel lines_p8 (lms graded)
a. the slope of m is - 3/2
b. the slope of n is - 5/3
c. the slope of n is 3/2
d. the slope of p is - 5/2

Explanation:

Step1: Recall slope formula

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$.

Step2: Calculate slope of line \(m\)

Let's take two points on line \(m\) say \((-2,7)\) and \((0, - 2)\). Then \(m_m=\frac{-2 - 7}{0-(-2)}=\frac{-9}{2}=-\frac{9}{2}\).

Step3: Calculate slope of line \(n\)

Take two points on line \(n\) say \((-5,0)\) and \((0, - 2)\). Then \(m_n=\frac{-2 - 0}{0-(-5)}=-\frac{2}{5}\).

Step4: Calculate slope of line \(p\)

Take two points on line \(p\) say \((4,5)\) and \((10,5)\). Then \(m_p=\frac{5 - 5}{10 - 4}=0\).

Step5: Calculate slope of line \(q\)

Let's assume two points on line \(q\) (not clearly - labeled in the problem - statement, but if we consider the general concept of slope - calculation). If we assume two points \((x_1,y_1)\) and \((x_2,y_2)\) on line \(q\) such that \(m_q=\frac{y_2 - y_1}{x_2 - x_1}\). If we assume the points based on the grid and the line's orientation, for example, if we consider two points on line \(q\) such that when \(x\) changes by \(3\), \(y\) changes by \(5\) in the negative \(y\) - direction. Then \(m_q =-\frac{5}{3}\).

Answer:

B. The slope of \(q\) is \(-\frac{5}{3}\)