Final answer:
The slope of a line is calculated as the rise over the run between two points on the line. The slope and y-intercept (point where the line crosses the y-axis) are fundamental in determining the shape of a straight line in algebra.
Step-by-step explanation:
The slope of a straight line on a graph is an important concept in algebra that shows the steepness and direction of the line. It can be calculated by the formula m = (rise)/(run), where 'm' represents the slope, 'rise' is the vertical change, and 'run' is the horizontal change between two points on the line.
In Figure A1, the line has a slope (m) of 3, indicating that for every 1 unit increase along the x-axis (horizontal), there is a 3 unit increase along the y-axis (vertical). The line intersects the y-axis at the point (0, 9), which is known as the y-intercept (b). This point shows where the line crosses the vertical y-axis when the value of x is 0.
To demonstrate the calculation of slope with a real-world example: suppose you're examining an air density graph, and you want to find the slope between two points, one at an altitude of 4,000 meters and the other at 6,000 meters. You would calculate the vertical change (difference in air density) and horizontal change (change in altitude) between these points to find the slope.