GT.5 investigate properties of points, lines and line segments in the co-ordinate plane so that[br]they can:[br]a. find and interpret: distance, midpoint, slope, point of intersection, and slopes of parallel[br]and perpendicular lines[br]b. draw graphs of line segments and interpret such graphs in context, including discussing[br]the rate of change (slope) and the y intercept[br]c. find and interpret the equation of a line in the form y = mx + c; y – y1[br] = m(x – x1[br]); and[br]ax + by + c = 0 (for a, b, c, m, x1[br], y1 ∈ ℚ); including finding the slope, the y intercept, and[br]other points on the line

A line graph is a type of chart used to display information as a series of data points connected by straight line segments. It is typically used to visualize data that changes over time or to illustrate trends within data sets. The x-axis of a line graph usually represents the independent variable (e.g., time), while the y-axis represents the dependent variable (e.g., quantity, value, etc.).[br][br]Interpolation in the context of a line graph refers to the process of estimating unknown values within the range of a discrete set of known data points. When interpolation is performed on a line graph, it is typically represented by straight lines between the known data points. This method assumes a linear relationship between the points for simplicity and ease of interpretation, which is why the interpolation is not curved.[br][br]The decision not to use curved interpolation (such as spline interpolation or polynomial interpolation) in basic line graphs is mainly for simplicity and clarity, particularly when the primary goal is to show trends or changes over time without assuming complex relationships between data points. Curved interpolation requires additional assumptions about the data's behavior between points and can introduce complexity that might not be justified by the data or the analysis's objectives. However, for more sophisticated analyses where the underlying relationships between data points are known to be non-linear, curved interpolation techniques can be applied to more accurately reflect these relationships.