 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that for the given graph find the simplified ratio of vertical side length to the horizontal side length and explain how these ratios relate to the slope of line. We know that the simplified ratio of the vertical side length to the horizontal side length of each similar triangle formed by the slope of line is equivalent to the absolute value of the slope. With this key idea let us proceed to the solution. Now let us see the given graph a non-vertical straight line and we have given points that is 0, 9, 2, 6 and 6, 0 that is points given on the line are 0, 9, 2, 6, 6, 0. In this question we need to find the simplified ratio of vertical side length to the horizontal side length and we need to explain how these ratios relate to the slope of line. So first we shall find slope of line by taking any two different points on the line. So let us take points 0, 9 and 2, 6. Now we know that slope of a line is given by changing y upon changing x. So change in y is given by 6 minus 9 upon change in x which is given by 2 minus 0. So we get the slope as minus 3 by 2 which is equal to minus of 1.5. So we get the value of slope as minus 1.5. Now we can see that the two triangles formed in graph have similar shape but different size. So the two triangles are similar. Now let us find the length of sides for the two triangles. First we take the larger triangle. Here we see that the vertical side length is equal to 1, 2, 3, 4, 5 and 6 that is 6 units. We have vertical side length is equal to 6 units and the horizontal side length will be equal to 1, 2, 3, 4 that is 4 units. So horizontal side length is equal to 4 units. Now for smaller triangle we see that the vertical side length is 1, 2, 3 that is 3 units and the horizontal side length is 1, 2 that is 2 units. So we write vertical side length is 3 units and horizontal side length is 2 units. Now we find the ratio of vertical side length to horizontal side length for two triangles. For larger triangle we have ratio which is given by vertical side length upon horizontal side length which is given by vertical side length that is 6 units upon horizontal side length that is 4 units. So we get 3 by 2 which is equal to 1, 5. Similarly for smaller triangle we have ratio vertical side length upon horizontal side length that is for smaller triangle we have the vertical side length as 3 units upon horizontal side length that is 2 units. So we get 1.5 as the ratio. In both the cases we have the ratio as 1.5. From the key idea we know that the simplified ratio of the vertical side length to the horizontal side length of each similar triangle formed by the slope of line is equivalent to the absolute value of the slope and here we know that the slope is given by minus of 1.5. So we can say absolute value of slope would be equal to modulus of minus of 1.5 that is 1.5. Thus we can say that the ratio of vertical side to horizontal side each similar triangle is equivalent to absolute value of the slope which is the required answer This completes our session. Hope you enjoyed this session.