This preview shows pages 1–4. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Basic Algebra Review for Math 1441 Introduction On your first day of Math 1441, you will take a Basic Algebra Exam. You should pass this exam in order to stay in the course. This material will help you review this elementary material in advance of the first day. If you cannot master these algebra skills, you should instead take Math 1400. These skills and more advanced skills will be heavily used in Math 1441. 1 Slope Recall that slope m is defined as rise run or change in y change in x . Rise is the distance traveled vertically and is positive if traveling up (in the positive y direction). Run is the distance traveled horizontally and is positive if traveling right (in the positive x direction). We estimate the slope of a line by drawing horizontal and vertical lines and estimating rise and run. Example: Approximate the slope of the given line. Solution: We draw in horizontal and vertical lines and estimate the run as 2 and the rise as 1. This gives an approximate slope of 1 2 . Note: If we had traveled in the other direction, we would estimate the run to be 2 and the rise to be 1, giving the same answer of 1 2 . Try the following problems. The answers are in the solution section. 1. Approximate the slope of the given line: 2. Approximate the slope of the given line: 2 Lines A line which goes through points ( x 1 , y 1 ) and ( x 2 , y 2 ) has slope m = change in y change in x = y 2 y 1 x 2 x 1 . If a line has slope m and goes through point ( x 1 , y 1 ), we call an arbitrary point on the line ( x, y ) and get that m = y y 1 x x 1 . Rewriting, we get the usual form y y 1 = m ( x x 1 ). Example: Find the line through points (2 , 3) and (1 , 4): The slope is m = 4  3 1 2 = 7 1 = 7. To find the equation, we can use either point. Using the point (2 , 3), we get y  3 = 7( x 2). 2 The equation of the line with slope m and y intercept b is y b = m ( x 0) or y = mx + b . (Recall: Since points on the y axis have x = 0, a y intercept of b indicates that point (0 , b ) is on the line.) Try the following problems. Recall that parallel lines have the same slopes. The answers are in the solutions section. 1. Find the equation of the line through points (4 , 2) and ( 1 , 3). 2. Find the equation of the line with x intercept 3 and y intercept 2. 3. Find the equation of the line that goes through the point (2 , 3) and is parallel to the line 2 x + 6 y = 1. 3 Exponents When you get confused about the rules for exponents, think about what the exponent means. Example: x 4 x 2 = ( xxxx )( xx ) = xxxxxx = x 6 . The exponents are added. Example: ( x 4 ) 2 = ( x 4 )( x 4 ) = ( xxxx )( xxxx ) = xxxxxxxx = x 8 . The exponents are multi plied....
View
Full
Document
This note was uploaded on 06/21/2011 for the course MTH 150 taught by Professor Marioborha during the Summer '11 term at Moraine Valley Community College.
 Summer '11
 MarioBorha
 Calculus, Algebra

Click to edit the document details