Question

11 compare finding the slope using a table and using a graph.

Explanation:

To find the slope using a table, we select two ordered pairs \((x_1, y_1)\) and \((x_2, y_2)\) from the table and use the formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\). For a graph, we identify two points on the line, determine the "rise" (change in \(y\), \(\Delta y\)) and "run" (change in \(x\), \(\Delta x\)) between them, and then calculate the slope as \(m = \frac{\text{rise}}{\text{run}}=\frac{\Delta y}{\Delta x}\). Both methods rely on the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\), but a table provides discrete data points while a graph shows a continuous line, so we pick points from the graph (often easier to use grid - aligned points for simplicity).

Answer:

• Using a Table:
• Select two rows (ordered pairs \((x_1,y_1)\) and \((x_2,y_2)\)) from the table.
• Calculate the slope using \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
• Using a Graph:
• Identify two points \((x_1,y_1)\) and \((x_2,y_2)\) on the line.
• Calculate the "rise" (\(\Delta y=y_2 - y_1\)) and "run" (\(\Delta x=x_2 - x_1\)).
• Find the slope as \(m=\frac{\text{rise}}{\text{run}}=\frac{\Delta y}{\Delta x}\).
• Both methods use the same slope formula, but a table has discrete data and a graph shows a continuous line (easier to use grid - based points on a graph).