Week 4 Notes, Intermediate Algebra
Week 4 Notes, Intermediate Algebra MA 0103
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This 3 page Class Notes was uploaded by Liyah Notetaker on Thursday February 11, 2016. The Class Notes belongs to MA 0103 at Mississippi State University taught by Jonathan Eaton in Fall 2016. Since its upload, it has received 34 views. For similar materials see Intermediate Algebra in Math at Mississippi State University.
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Date Created: 02/11/16
Aliyah Alexander Intermediate Algebra The Meaning of Slope and yIntercept. in the Context of Word Problems. In the equation of a straight line (when the equation is written as "y = mx + b"), the slope is the number "m" that is multiplied on the x, and "b" is the yintercept, where the line crosses the yaxis. Solve for y. Use the resulting equation to find the slope of line. –3x + y = 9 Step 1 Using the Addition Property, add 3x to both the sides. –3x + 3x + y = 3x + 9 Simplify. y = 3x + 9 Step 2 The equation is in the slope–intercept form, y = mx + b Hence, the slope is 3. What is the slope of the line with equation 3x + 2y = 8? In order to find the slope, it is simplest to put this line equation into slopeintercept form. If I rearrange this line to be in the form "y = mx + b", it will be easy to read off the slope m. So I'll solve: 3x + 2y = 8 2y = –3x + 8 –3 y = ( /2 ) x + 4 –3 Then the slope is m = / .2 Find the slope and yintercept of the line with equation 2x – y = 5. I'll solve for "y =": 2x – y = 5 2x = y + 5 2x – 5 = y Then y = 2x – 5, and, from the slopeintercept form of y = mx + b, I can see that: the slope is m = 2 and the yintercept is b = –5. Find the slope and yintercept of the line with equation x – 2y = 5. I'll solve for "y =": x – 2y = 5 x = 2y + 5 x – 5 = 2y ( / ) x – ( / ) = y 2 2 1 5 Then y = ( / 2 x – ( / 2, so: the slope is m = / and the yintercept is b = / . –5 2 2 Find the slope and yintercept of the line with equation 4x + 5y = 12. I'll solve for "y =": 4x + 5y = 12 5y = – 4x + 12 y = ( / 5) x + ( / 5) –4 12 Then the slope is m = / and t5e yintercept is b = / . 5 Point–slope form. : the equation of a straight line in the form y − y = m(x − x ) 1here m is the1 slope of the line and (x , y1) a1e the coordinates of a given point on the line — compare slope intercept form. A line passes through the point (4, –3) and has slope m = 1. Find the equation in point–slope form. Step 1 The point–slope form of the equation for a line passing through the point (x ,y ) is given b1: 1 Assuming (4, –3) = (x , y )1and1m = 1 and substituting the values, we get: Step 2 Simplify. If you need further help, seek your intermediate algebra book. Hope this helps:)
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