Question

lets chat- parallel vs. perpendicular
parallel: keep the slope, change the y int
perpendicular: flip the slope, change sign, change, any y int
prediction:
now count...over/up
1st slope= m:
2nd slope=
3rd =
determine which lines, if any, are parallel? explain.

Explanation:

Step1: Recall slope - formula

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

Step2: Calculate slope of first line

For the line passing through $(-4,1)$ and $(-3, - 2)$, $x_1=-4,y_1 = 1,x_2=-3,y_2=-2$. Then $m_1=\frac{-2 - 1}{-3-(-4)}=\frac{-3}{1}=-3$.

Step3: Calculate slope of second line

For the line passing through $(-2,1)$ and $(-1,-2)$, $x_1=-2,y_1 = 1,x_2=-1,y_2=-2$. Then $m_2=\frac{-2 - 1}{-1-(-2)}=\frac{-3}{1}=-3$.

Step4: Calculate slope of third line

For the line passing through $(2,3)$ and $(3,-1)$, $x_1=2,y_1 = 3,x_2=3,y_2=-1$. Then $m_3=\frac{-1 - 3}{3 - 2}=\frac{-4}{1}=-4$.

Step5: Determine parallel lines

Parallel lines have equal slopes. Since $m_1=-3$ and $m_2=-3$, the lines passing through $(-4,1)$ and $(-3,-2)$ and the line passing through $(-2,1)$ and $(-1,-2)$ are parallel.

Answer:

The lines passing through $(-4,1)$ and $(-3,-2)$ and the line passing through $(-2,1)$ and $(-1,-2)$ are parallel because they have the same slope ($m=-3$).