Expert: Michael Tadesse - 8/21/2010

Question
Show all calculations for the following questions:

     1. Slope-Intercept form:   y = -2x - 6   

     Identify three points on the graph where this equation would run through using the substitution method of x or y. Show all work at arriving at each point. You will receive 25 points for your correct answers and 25 points for showing all work at arriving at your results.



2. What is the equation of a line running through the following points?: (6,4) and (-6,8)

What is the slope of this equation? What is the y-intercept of this equation?

Name an equation parallel to this equation?    perpendicular?

In each of the following two problems are the following lines AB and CD parallel, perpendicular or neither?

a) A(1,1), B(-1,2) and C(1,-1), D(0,-3)

b) A(0,4), B(-2,-2) and C(1,-1) and D(0,-4)

If an equation passed through the following points (1,6) and (9,10), the slope would be 1/2.

Identity two points where if an equation passed through you would get:

a) a slope of -3/4

b) a slope of 3

b) a slope of 0

Convert the following two equations to slope-intercept form:


a) 1/3x + 3 = 3/4y

b) 3x -4y - 20 = 0  

Answer
Hello Rebecca
For this problem you just have to substitute any value of X and find the value of Y as long as the domain of the equation is all real numbers.
Let’s take 0, 3 and 5
Y(0) = 0-6
Y = -6
{0, -6}
Y(3) = -6 – 6
Y = -12
{3, -12}
Y(5) = -10 – 6
Y = -16
{5, -16}
2. What is the equation of a line running through the following points?: (6,4) and (-6,8)

First compute the slope of the line
It is -1/3
Y = (-1/3)X + b
To find b just substitute one of the coordinates.
4 = (-1/3)*6 + b
4 = -2 + b
B = 6
So the equation of the line is
Y = (-1/3)X + 6
By the way the slope intercept of the equation is 6 where X = 0
Name an equation parallel to this equation?    perpendicular?

To find a line which is parallel to this equation, observe that parallel lines have equal slopes.
So Y = (-1/3)X + b
They only differ in their y intercepts.
So take any coordinate and substitute it in the equation to find b
I chose {1, 2}
2 =  (-1/3)*1 + b
B = 7/3
So the equation of the line is;
Y = (-1/3)X + 7/3
To find a line which is perpendicular, observe that perpendicular lines have slopes whose product is -1
Therefore the slope of any perpendicular line the above line has a slope 3 RIGHT check the product.
Y = 3X + b
Take any coordinate you like, {0, 1}
1 = 0 + b
B = 1
Y = 3X + 1
I’ve almost solved all of it you should try the remaining and if you get stumped don’t hesitate to ask questions.
Thankz
Michael