How are line graphs used to show how two variables are related?
1 answer:
A line graph is characterized by a correlation in the form of a line. The dependent variable is placed on the y-axis and the independent variable is on the x-axis. You can see their relation in terms of the slope. By definition, the slope is the ratio of the change of the y-coordinates to the change of the x-coordinates (Δy/Δx). Visually, you can determine the relationship of the variables by the orientation of the line as shown in the graph. If the slope is increasing, it means that the two variables are increasing together. If the slope is decreasing, it means that when x increases, y decreases. In other words, they are inversely proportional. You can also note the extent of change by knowing which has the greater slope.
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Answer:
Part A
The rotation of the point (x, y) 180° about the origin gives the point (-x, -y)
Therefore, we have the points, ΔLMN, L(1, 1), and M(2, 2), and N(3, 3)
The coordinates of the vertices of the image, ΔL'M'N' are L'(-1, -1), and M'(-2, -2), and N'(-3, -3)
Please find attached the graph of triangle ΔLMN and ΔL'M'N'
Part B
The lines drawn through L and L' and through M and M' are colinear
Part C
A line is defined by two points, such as <em>L </em>and <em>M.</em> Rotation of a line through 180° about the origin will give an image location on the same path as the extension of the original line.
The third point, <em>N</em>, however, defines a plane, and the rotation of a plane by 180° will give an image which is turned upside down with regards to the preimage
Therefore, a trough in the preimage becomes a peak in the image and the lines drawn through N and N' crosses the colinear lines drawn throgh M and M' and L and L'
Step-by-step explanation:
