Graph A bowling ball was set into motion on a fairly smooth...

Graph A bowling ball was set into motion on a fairly smooth level surface, and data were collected for the total distance covered by the ball at each of four times. These data are shown in the table. (a) Plot the data points on a graph. (b) Use a ruler to draw a straight line that passes as close as possible to the data points you have graphed. (c) Using methods you were taught in algebra, calculate the value of the slope, $m$, and find the value of the intercept, $b$, of the line you have sketched through the data.

Graph A bowling ball was set into motion on a fairly smooth level surface, and data were collected for the total distance covered by the ball at each of four times. These data are shown in the table.
(a) Plot the data points on a graph.
(b) Use a ruler to draw a straight line that passes as close as possible to the data points you have graphed.
(c) Using methods you were taught in algebra, calculate the value of the slope, $m$, and find the value of the intercept, $b$, of the line you have sketched through the data.

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Key Concepts

Y-intercept

The y-intercept is the point where the line crosses the y-axis in a graph. It represents the value of the dependent variable when the independent variable is zero, providing a starting point for the linear relationship described by the equation.

Slope

Slope is a measure of the steepness or rate of change of a line, defined as the ratio of the 'rise' (vertical change) to the 'run' (horizontal change) between two points on the line. It quantifies how much the dependent variable changes for a unit change in the independent variable.

Line of Best Fit

The line of best fit is a straight line drawn through a scatter plot of data that best represents the overall trend of the data. It minimizes the distance between itself and all the data points and is often used to predict values and understand the relationship between variables.

Plotting on a Coordinate Plane

This concept involves using a system of axes to represent data points graphically. It requires assigning one variable to the horizontal (x-axis) and another to the vertical (y-axis) and plotting each pair of values accurately. This method provides a visual representation of the relationship between variables.

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