write an equation of a line that is parallel to the line created by (2,4) and (-4,3) and passes through (10,-2)

Question

its an equation of an line that i need help in please and thank you

Answer 1

Hi Edward, start by finding the slope of the line given the two points: (2, 4) and (-4, 3).

 

Slope of the line:

 

Slope = (4 - 3) / (2 - (-4) = 1 / 6

 

Use the point-slope form to find the line of the two points:

 

y - y₁ = m * (x - x₁)

 

Substitute for y₁, x₁, and m:

 

m = 1 /6

 

y₁ = 4

 

x₁ = 2

 

y - 4 = 1 / 6 * (x - 4)

 

y - 4 = 1 / 6 * x - 4 / 6

 

Add 4 to both sides of the equation:

 

y = 1 / 6 * x + 20 / 6

 

Reduced:

 

y = 1 / 6 * x + 10 / 3

 

A line parallel to the above line will have the same slope, 1 / 6.

 

Use the point-slope form of the line again with the slope, m, equal to 1 / 6, and the given point: (10, -2)

 

m = 1 / 6

 

y₁ = -2

 

x₁ = 10

 

y - (-2) = 1 / 6 * (x - 10)

 

y + 2 = 1 / 6 * x  - 10 / 6

 

Subtract 2 from both sides of the equation:

 

y = 1 / 6 * x - 22 / 6

 

Reduced:

 

y = 1 / 6 * x - 11 / 3

 

Questions?