logo for solving-math-problems.com
leftimage for solving-math-problems.com

Developmental Math

by Maribeth
(Draper, South Dakota)











































Find the equation of line b described below, in slope intercept form.

Line a is parallel to line b.

Line a passes through points (5,7) & (-1,-2).

Line b passes through points (11,-5).

Comments for Developmental Math

Click here to add your own comments

Aug 18, 2013
Linear Equation
by: Staff


Answer

Part I

Since line b is parallel to line a, the slope of
line b is equal to the slope of line a.



Determine the slope of line “a”.

slope = "rise" over "run", or "rise" DIVIDED BY "run"

slope = (change in "y" values)/(change in "x" values)

slope = Δy / Δx

slope = (y₂ - y₁)/(x₂ - x₁)



Slope of a line (m) =  (y₂ - y₁)/(x₂ - x₁)






The x-y coordinates for the two points for Line “a” are


However, these two points are must be listed in the proper order (left to right).

The two points should be listed as (-1, -2) and (5, 7) because the slope will be calculated as the change of "y" when x increases. In this case "x" will increase from -1 to 5 (left to right).



Calculation of the slope for Line “a”

Points: Left and Right

(-1, -2) and (5, 7)

(x₁, y₁) and (x₂,y₂)

x₁ = -1
x₂ = 5

y₁ = -2
y₂ = 7

slope = (y₂ - y₁)/(x₂ - x₁)

slope = (7 - (-2))/(5 - (-1))

slope = (7 + 2)/(5 + 1)

slope = (9)/(6)

slope = 3/2




-----------------------------------------------------------

Aug 18, 2013
Linear Equation
by: Staff


-----------------------------------------------------------



Part II



Compute the slope (m) of line 'a' where

 y₂ = 7, y₁ = -2

 x₂ = 5, x₁  = -1





Write the equation of line “b”.

The Point-Slope Form


Point-Slope Form: (y - y₁) = m (x - x₁) 


This format uses a single known point (x₁,y₁) and the slope m (which is also a known value)

From the problem statement:

m (the slope) = 3/2

single known point (x₁,y₁) = (11,-5)

x₁ = 11

y₁ = -5

(y - y₁) = m (x - x₁)

(y - (-5)) = (3/2)*(x - 11)



-----------------------------------------------------------

Aug 18, 2013
Linear Equation
by: Staff


-----------------------------------------------------------



Part III



Since line 'a' and line 'b' are parallel, substitute the following values into the point slope formula for line 'b'

 slope (m) of line 'a' = 3/2 

 x-y values of a single point on line 'b': 

    y₁ = -5

    x₁  = 11





Point Slope Form of Equation for Line “b”: (y + 5) = (3/2)*(x - 11)



The Slope Intercept Form

Slope Intercept Form


y = mx + b

(y + 5) = (3/2)*(x - 11)

2*(y + 5) = 2*(3/2)*(x - 11)

2y + 10 = 3x - 33

2y + 10 - 10 = 3x - 33 - 10

2y + 0 = 3x - 43

2y = 3x - 43

2y / 2 = (3x - 43) / 2

y = (3/2)x - 43/2



Slope Form of Equation for Line “b”: y = (3/2)x - 43/2







-----------------------------------------------------------

Aug 18, 2013
Linear Equation
by: Staff


-----------------------------------------------------------



Part IV



 Solve the point slope formula for y




Graph of linear equations for line 'a' and line 'b'

line 'a'

     y = (3/2)x - 1/2

line 'b'

     y = (3/2)x - 43/2








Thanks for writing.

Staff
www.solving-math-problems.com


Click here to add your own comments

Join in and write your own page! It's easy to do. How? Simply click here to return to Math Questions & Comments - 01.



Copyright © 2008-2015. All rights reserved. Solving-Math-Problems.com