1. Investigation 8:06 | Straight line graphs<br />274320020320Please use the Assessment Grid on the<br />following page to help you understand<br />what is required for this Investigation.<br />On this number plane we have graphed two<br />‘families’ of lines; one set red, one set blue.<br />1 (a) How are the red lines alike? <br />The red lines are parallel lines.<br />(b) How are the red equations alike?<br />All the red equations have -x in the equation.<br />2 (a ) How are the blue lines alike?<br />The blue lines are also parallel.<br />(b ) How are the blue equations alike?<br />They all have 2x in the equations.<br />3 (a ) Which lines intersect at the origin?<br />The green line: y=1x, the blue line: y=2x and the red line: y=-x intersect at the origin.<br />(b) How are the equations of these lines alike?<br />365760092710They all don’t have the constant number, like y=2x+3, 3 is the constant number.<br />4 (a ) Which lines would be parallel to y = − x + 4? (Graph this line.)<br />A: y=− x + 4 is parallel to all the red lines: y=− x + 1,<br />y=− x , y=− x -1 and y=− x -3<br />(b) Which lines would be parallel to y = 2x + 1? (Graph this line.)<br />A: y = 2x + 1 is parallel to all the blue lines: y = 2x +4, y = 2x and y = 2x -4<br />205740085090<br />5 The equation of a line can be written in different ways. All of those graphed here are written in the form y = mx + b.<br />(a)Would all lines that have a negative<br />x term (eg y = − x + 4)<br />(slope down) or increase (slope up) as x increases in value?<br />A: Lines with a negative x term decrease when x increases the value, the line will slope down. Because in a number plane, the negative parts are at the bottom, so it will slope down. <br />(b) Would all lines that have a positive x term (eg y = 2x + 1) increase or decrease?<br />A: Lines with a positive x term increase when x increases the value, the line will slope up. Because in a number plane the positive part is at the top, so of course it will slope up.<br />(c) By investigating these graphs, can you find some connection between the constant b in each equation (eg y = 2x + 4) and the graph of the line?<br />When b is bigger then 0 (positive), the dot should be at the top part of the number plane, when b is smaller then 0 (negative）， the dot should be at the bottom part of the number plane. And when b equals zero, it go through from the middle of the number plane, which is from zero.<br />X-1-2-3y20-2<br />y = 2x + 4<br />x=-1, -2+4=y<br />x=-2, -4+4=y<br />x=-3, -6+4=y<br />
