Final answer:
A line joining 2 points that travels up and to the right has a positive slope. This positive slope signifies an upward tilt and a positive relationship between the x and y variables on a graph.
Step-by-step explanation:
If a line joining 2 points goes up and to the right, the slope is positive. When the slope of a line increases, graphically, this results in a steeper ascent, meaning a steeper upward tilt. In contrast, when the slope decreases, the line flattens out. Whether the slope is originally positive or negative, these changes are consistent - a higher positive slope equates to a steeper line, while a smaller positive slope suggests a less steep, more gradual incline.
A negative slope that is more significant in absolute value indicates a steeper decline, while a less negative slope suggests a more gradual decline. A slope of zero corresponds to a horizontal flat line, and a slope that is undefined, due to vertical lines not having a measurable run, is described as having an infinite slope.
The value of the slope is vital in depicting how the line moves on a graph. Specifically, a positive slope means the line rises as you move from left to right, indicating a positive relationship between the x and y variables. This relationship is especially important in various fields, such as economics, where it can illustrate how one variable changes in response to another.