Find the Slopes of 2 Lines

Question

Given below are descriptions of two lines.

Line 1: Goes through (-4,1) and (4,3)

Line 2: Goes through (0,5) and (4,6)

The slope of Line 1 is    

The slope of Line 2 is $m$

Answer 1

NOTE: The shortest distance between two points is a straight line.

The Equation for Slope requires two points: m = (y₂ - y₁)/(x₂ - x₁),

where point 1 is (x₁, y₁) and point 2 is (x₂, y₂)

For Line 1, let (-4,1) be point 1, therefore, (x₁= -4, y₁= 1)

and let (4,3) be point 2, therefore, (x₂= 4, y₂= 3)

Now, calculate the slope of Line 1 using the Equation of Slope, m = (y₂ - y₁)/(x₂ - x₁)

m_{line 1} = (3 - 1)/(4 - -4) = 2/8 = 1/4

Now, apply the method above to determine the slope of Line 2,

m_{line 2} = ( - )/( - ) =

Answer 2

Slope of a line

m = (y2-y1)/( x2 -x1)

For line 1

y1 = 1 , y2 = 3

x1 = -4 , x2 =4

m = (3-1)/ ( (4--4) = 2/8 = 1/4

For line 2

y1 = 5 , y2 = 6

x21 = 0 , x2 =4

m= (6-5)/(4-0) = 1/4

Two lines have same slope and so are parallel

Answer 3

Use the definition of sliope:

m = (y₁ - y₂) / (x₁ - x₂)