Paper Topic:

Algebra

br JavaScript is required for your course . ensure JavaScript is enabled in your browser preferences

Seminar on Slope , Equations of Lines and Systems of Equations

To earn seminar credit for this unit , complete one of the following options below

Option 1 : Participate in a synchronous seminar (Note : Students are encouraged to attend seminar but the student may complete Option 2 instead of attending seminar

The seminar 's is "Slope , Equations of Lines and Systems of Equations " complete the Unit 4 reading before attending the seminar session in to be familiar with

the necessary terminology and concepts . Concepts and example problems will be discussed supplementing the material covered by the textbook

Option 2 : Complete the entire problem set below 1 . Find the slope of the line that passes through the points (4 , -7 ) and (-2 , -5

Solution : The slope of the line m is calculated below

m (-5 ) - (-7 (-2 ) - 4 2 (-6 - (1 /3

2 . Find the equation of the line with a slope of -5 and passes through the point (2 , -4

Solution : Equation of the line can be written as

y - (-4 (-5 (x - 2

i .e . y 4 -5x 10

i .e . y -5x 6

3 . Write an equation of the line that passes through (0 , -4 ) and is parallel y (3 /4 )x 2 . Write the answer in slope-intercept form

Solution

As this lime is parallel to y (3 /4 )x 2 therefore , its slope will be

As , it passes through (0 , -4 , therefore , its equation can be written as

y - (-4 (3 /4 (x - 0

i .e . y 4 (3 /4 )x

i .e . y (3 /4 )x - 4

4 . Solve the system of equations by substitution

x 2y 9

3x - y 13

Solution

Given , x 2y 9 (1

3x - y 13 (2

From (2 , y 3x - 13 (3

By (3 ) in (1 , x 2 (3x - 13 9

i .e . x 6x -26 9

i .e . 7x 35

Hence , x 5

Putting x 5 in (3 , y 3 5 - 13 2

Therefore , the solution is x 5 and y 2

5 . Solve the system of equations by substitution

4x - 3y 1

12x - 9y 3

Solution

Given , 4x - 3y 1 (1

12x - 9y 3 (2

From (2 , y (1 /9 (12x - 3 (3

By (3 ) in (1 , 4x - 3 (1 /9 (12x - 3 1

i .e . 4x - 4x 1 1

i .e . 1 1

This is an identity . This has resulted because equations (1 ) and (2 ) are identical . Therefore , no unique solutions rather there are infinitely many solutions for this set of simultaneous equations . The solution is a straight line in x-y plane

The solution will be of the form y (1 /3 (4x - 1...

2 pages

30.0 KB

Free sing-up