Practice College Algebra Online

Introduction :

College algebra is one important topic in mathematics. College algebra is used for the known quantities to determine the unknown quantities. In place of numbers, sometimes letters can be used. It includes the different topics such as polynomials, equation, expression, equation of a line, Cramers rule and slope of a line. Let us discuss some practice problems in college algebra through online.


Example problems for practice college algebra online:


Example 1:

Factorize: 45xy -18ya + 60xb -24ab using factor by group

Solution:

Step 1:

Given expression 45xy- 18ya + 60xb -24ab

Step 2:

Given expression in the standard form ax² + bx + c = 0

45xy- 18ya + 60xb -24ab = 0

Step 3:

Groups the terms

45xy- 18ya + 60xb -24ab = 0

(45xy + 60xb) - (18ya – 24ab) = 0

Step 4:

Determine the greatest common factor for the expression given

15x (3y – 4b) – 6a (3y – 4b) = 0

(15x – 6a) (3y – 4b) (3y – 4b) = 0

Solution to the given equation is (15x – 6a) (3y – 4b) = 0.

Example 2:

Find the slope of a line for the given points (4, 6) and (8, 9)

Solution:

For finding the slope of a line, we use this formula

`m = (y_2 - y_1)/(x_2 - x_1)`

Here the given points of (x1 , y1) and (x2, y2) are substituted in the formula.

`m = (9 - 6)/(8 - 4)`

`m = (3)/(4)`

`m = (3)/(4)`

Solution to the slope of a line is m = 3/4.

Example 3:

Find the equation of a line which passes through the line (-3,4) with slope of -3.

solution:

Given:

x1= -3, y1 = 4 and slope m = -3

Equation of a point slope form equation is

y - y1 = m (x - x1)

y - 4 = -3(x - (-3))

y - 4 = -3(x + 3)

y - 4 = -3x -9

y = -3x -5.

Solution to the equation of a line is y = -3x - 5

Having problem with Standard Form of the Equation of a Line keep reading my upcoming posts, i will try to help you.

Practice problem for college algebra online:


Some example practice problems for college algebra online

1). Factorize the given expression by using the factor by group method.

30xy + 40xb - 12ay - 16ab

Solution: (10x – 4a) (3y – 4b) = 0.


2). Solve the system of equation with two variables equations.

x + y = 10                       → (1)
3x - y = 6                       → (2)
Solution of the equation is (x and y) is (4, 6)

3). Find the slope of a line for the given points (5, 6) and (8, 9)

Solution: m = 1

4). Find the equation of a line which passes through the line (-5,6) with slope of -2.

Solution: y = -2x -4