2-7 Analyze Linear Equations y = mx PDF

2-7 Analyze Linear Equations: y = mx This material may be reproduced for licensed classroom use Copyright © McGraw Hill only and may not be further reproduced or distributed. Learn Note : linea...

2-7 Analyze Linear Equations: y = mx This material may be reproduced for licensed classroom use Copyright © McGraw Hill only and may not be further reproduced or distributed. Learn Note : linear equation y = mx Very important , you should always keep it in mind The form of linear equation is y = mx + b ( we will analyze it next lesson) If b = 0 linear equation form will be y = mx ( m indicates the slope ) When we graph this equation y = mx definitely the graph Will be straight line and passes through the origin ( 0 , 0 ) as shown in the figure aside Very important This material may be reproduced for licensed classroom use McGraw Hill | Direct Variation only and may not be further reproduced or distributed.  Note : Learn : When we want to move from The graph to equation we need how can move from a graph to equation To find : Step one : find a slope. Step two :since the graph passes Through P 134 the origin ( 0,0 ).the equation will be y = mx ( m indicates the slope ) 60 20 20 4 1 This material may be reproduced for licensed classroom use McGraw Hill | Direct Variation only and may not be further reproduced or distributed.  Example P 135 The solution : Step one : find the slope 4 −2 2 Slope = = 10 −5 5 Step two : substitute into equation y =mx 2 There fore , y= x 5 This material may be reproduced for licensed classroom use McGraw Hill | Direct Variation only and may not be further reproduced or distributed.  P 135 NOTE : Example 2 When we want to graph an equation we need : Graph an equation of the form y = mx Step one : draw a table Step two : assign two value ( it’s optional ) for x then plot these point x 0 1 y=-3(0)=0 y 0 -3 y=-3(1)= −3 Then plot these point into coordinate plane This material may be reproduced for licensed classroom use McGraw Hill | Direct Variation only and may not be further reproduced or distributed.  This material may be reproduced for licensed classroom use McGraw Hill | Direct Variation only and may not be further reproduced or distributed.  P 136 The solution: We need to find the equation we already Have a table so The solution : 50 −25 25 Slope = = = 12.5 120 − 90 30 4 −2 2 a. Slope = = 4 −3 1 Since The relationship is proportional so the b. y = 30x graph will be straight line and passes through the origin ( 0 , 0 ) the equation will be y = mx The equation , y = 12.5x This material may be reproduced for licensed classroom use McGraw Hill | Direct Variation only and may not be further reproduced or distributed.  P 136 P 137 140 140 4 2 The solution : 70 x 0 2 y 0 -1 70 1 2 𝑦=− 1 0 =0 y=− 2 = − = −1 2 2 2 This material may be reproduced for licensed classroom use McGraw Hill | Direct Variation only and may not be further reproduced or distributed.  This material may be reproduced for licensed classroom use McGraw Hill | Direct Variation only and may not be further reproduced or distributed.  P 137 P 137 The solution : 48 − 24 24 a. Slope = = = 12 4−2 2 The equation will be y = 12 x The solution : Franco made this graph incorrectly b. A graph will be a straight line and passes through Because we know when the value of The origin ( 0 , 0 ) The slope is negative the graph must be decreased in this example the graph is increased Therefore , Franco made this graph incorrectly This material may be reproduced for licensed classroom use McGraw Hill | Direct Variation only and may not be further reproduced or distributed.  P 138 P 138 The solution : The solution : x 0 1 x 0 1 y 0 -5 y 0 0.6 3 3 3 𝑦 =−5 0 =0 y = − 5 1 = −5 𝑦= 0 =0 y= 1 = = 0.6 5 5 5 This material may be reproduced for licensed classroom use McGraw Hill | Direct Variation only and may not be further reproduced or distributed.