Problem

Given below are descriptions of two lines. Line 1: Goes through $(0,7)$ and $(-2,-3)$ Line 2: Goes through $(-2,-4)$ and $(2,16)$ The slope of Line 1 is $m=$ The slope of Line 2 is $m=$ Finally, which of the following is true? Line 1 is parallel to Line 2. Line 1 is perpendicular to Line 2 Line 1 is neither parallel nor perpendicular to Line 2

Solution

Step 1 :Given below are descriptions of two lines.

Step 2 :Line 1: Goes through $(0,7)$ and $(-2,-3)$

Step 3 :Line 2: Goes through $(-2,-4)$ and $(2,16)$

Step 4 :The slope of a line is calculated by the formula \((y2 - y1) / (x2 - x1)\). We can use this formula to calculate the slopes of both lines.

Step 5 :If the slopes are equal, the lines are parallel. If the product of the slopes is -1, the lines are perpendicular. If neither of these conditions are met, the lines are neither parallel nor perpendicular.

Step 6 :Calculate the slope of Line 1: \(m1 = (7 - (-3)) / (0 - (-2)) = 5.0\)

Step 7 :Calculate the slope of Line 2: \(m2 = (16 - (-4)) / (2 - (-2)) = 5.0\)

Step 8 :The slopes of both lines are equal, which means the lines are parallel.

Step 9 :Final Answer: The slope of Line 1 is \(m= \boxed{5.0}\), the slope of Line 2 is \(m= \boxed{5.0}\), and \(\boxed{\text{Line 1 is parallel to Line 2}}\)

From Solvely APP
Source: https://solvelyapp.com/problems/41194/

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