Question

two points are given from each of two lines (l_1) and (l_2). without graphing the points, determine if the lines are parallel, perpendicular, or neither. express numbers as integers or simplified fractions.
(l_1:(-5, -4)) and ((5, 3))
(l_2:(-4, 0)) and ((6, 7))
part: 0 / 3
part 1 of 3
first determine the slope of each line. then compare the values of the slopes to determine if the line is parallel or perpendicular.
for line 1:
label the points.
(l_1:(-5, -4)) and ((5, 3))
((x_1,y_1)) ((x_2,y_2))
apply the slope formula:
(m=\frac{y_2 - y_1}{x_2 - x_1})

Explanation:

Step1: Calculate slope of $L_1$

Let $(x_1,y_1)=(-5,-4)$ and $(x_2,y_2)=(5,3)$. Using the slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}$, we have $m_1=\frac{3-(-4)}{5 - (-5)}=\frac{3 + 4}{5+5}=\frac{7}{10}$.

Step2: Calculate slope of $L_2$

Let $(x_1,y_1)=(-4,0)$ and $(x_2,y_2)=(6,7)$. Using the slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}$, we get $m_2=\frac{7 - 0}{6-(-4)}=\frac{7}{10}$.

Step3: Compare slopes

Since $m_1 = m_2=\frac{7}{10}$, the two lines are parallel.

Answer:

The lines $L_1$ and $L_2$ are parallel.