Explain why a straight line on graph shows a constant rate change.
Explain why a straight line on a graph shows a constant rate of change.?
When a straight line is plotted on a graph, it shows a constant rate of change because every point on the line has the same slope or gradient. The slope of a line represents how much the dependent variable (y) changes with respect to a change in the independent variable (x).
To understand why a straight line represents a constant rate of change, we can use the formula for slope, which is:
slope = (change in y) / (change in x)
Suppose we have two points on the line: (x₁, y₁) and (x₂, y₂). The change in y is given by y₂ - y₁, and the change in x is x₂ - x₁. Substituting these values in the formula, we get:
slope = (y₂ - y₁) / (x₂ - x₁)
If all points on the line have the same slope, it means that the change in y divided by the change in x is constant. In other words, for every unit increase in x, there is a fixed amount of increase or decrease in y. This consistent ratio of change in y to change in x gives us a straight line on the graph.
For example, let's say we have a line with a slope of 2. This means that for every unit increase in x, the corresponding y-value increases by 2. No matter which two points we choose on the line, the slope will always be 2, indicating a constant rate of change.
Therefore, a straight line on a graph shows a constant rate of change because all points on the line have the same slope, which represents the consistent ratio between the change in y and the change in x.
because the ratio of the change in y to the change in x is constant.
Draw any two right triangles whose diagonal is a section of the line, and they are similar, since the have common angles.