Final answer:
The slope formula for graphs, represented by the letter m in the straight line equation y = mx + b, determines the steepness of the line. A slope of 3 means for every 1 unit increase horizontally, the line rises by 3 units vertically. Slope is crucial for comparing how lines incline or decline on a Cartesian coordinate system.
Step-by-step explanation:
The slope formula for graphs is a vital concept in algebra that helps determine how steep a line is on a Cartesian coordinate system. The slope, represented by the variable m, indicates the rate at which the line rises or falls as you move along the x-axis (horizontal axis). The general equation for a straight line is y = mx + b, where m is the slope and b is the y-intercept, which is the point where the line intersects the y-axis.
In the context of the information provided, if a slope of a line on a graph is 3, it means that for every 1 unit increase in the horizontal direction (along the x-axis), there is a rise of 3 units in the vertical direction (along the y-axis). Therefore, if the line graph has a y-intercept of 9, the complete equation of this line would be y = 3x + 9, where 3 represents the slope (m) and 9 represents the y-intercept (b).
This formula can be used to compare different lines on the same graph. For instance, if another line has an equation y = -2x + 5, its slope would be -2, indicating that the line descends 2 units on the vertical axis for every 1 unit increase on the horizontal axis, and its y-intercept is 5.