Algebra 2 Part 9 Chapter 1

Service Description

There was only room for one question in the Second Section Exercise of Chapter 1 1-7 The answer to that interval notation is (- 4, 6) 1-8. The number line is five lines to the left of zero and nine lines to the right of zero; The thick line starting as a filled in circle or dot running with an arrow left from line left of zero with an arrow straight out left and then it is started at the 5th mark right of zero with a filled in circle or dot running with an arrow straight to the right; Therefore. the answer is (- eternity, - 1] U [5, eternity) 9 thru 12 solve for x and write the solution in interval notation 1-9. 2(x - 5) <_ 6x + 2 the answer is [ - 3. eternity), 1-10. - 6x + 7<_ 9 - 2(x - 3) the answer is [- 2, eternity) 1-11. 3x -7 > 8 v 5 -2x >_ 7 the answer is (- eternity, - 1] U (5, eternity) 1-12. -15 <_ 5 -2x <25 the answer is (-10,10] Now we are going to get into graphing starting with Linear Equations in Two Variables Usually, they are done on graph paper 1/4 inch cubes some are done in a graph of two lines with a sloped line marked with dotted line, but you can describe it to Grandma in the way she does. "A 'linear equation in two variables' can be simplified to the form Ax + By = C where A, B, and C are real numbers and A and B are not both 0. Solutions to such equations are ordered pairs (x, y). Although 'linear equations' in one variable usually have a single solution, infinite ordered pairs solve a linear equation in two variables. When the solutions are graphed in the x-y plane, they form a straight line." Example 1.15 ' Graph' the line 2x + 3y = 12. Solution "There are several ways to 'graph' a line. One that is often convenient is the 'intercept method'. We need only two points to determine the graph of the line. Finding the two intercepts is easy." 'y-intercept': set x = 0 2(0) = 3 y = 12---> y = 4 'x-intercept': set y = 0 2x + 3(0) = 12---> x =6 Therefore, using a vertex point at which three lines connect on a graph or graph piece of paper you can start at that vertex and count upward 4 spots marking a dot to use as the y line and count 6 spots as x and out from that vertex point the opposite line of x, then connect the two points with a third line finishing a triangle. That represents our 'Graph' of 2x + 3y = 12. (Grandma's Place of Natural Learning will start with 'Slope' next lesson.)