What is the slope of the Equation? y = 3/2x + 9
The Correct Answer and Explanation is:
The equation given is in the slope-intercept form, which is:
y = mx + b
In this equation:
- m represents the slope.
- b represents the y-intercept.
Comparing your equation to the slope-intercept form, y = (3/2)x + 9, you can see that the slope m is 3/2.
Explanation:
The slope of a line tells us how steep the line is, or how much the value of y changes when the value of x increases by 1. Specifically, the slope is a ratio of the vertical change to the horizontal change between two points on the line.
In this case, the slope m = 3/2 means that for every 2 units the x value increases, the y value increases by 3 units. This gives us a positive slope, indicating that the line rises as you move from left to right on the graph.
To better understand this:
- If you start at any point on the line, moving 2 units to the right (increasing x by 2) will result in an increase of 3 units in the y value. For example, if you were to start at the point (0, 9) — the y-intercept — and move rightward by 2 units, you would end up at the point (2, 12), because the y value has increased by 3.
This slope of 3/2 is useful when graphing the equation, as it dictates the steepness of the line and the direction of its slope. Since it’s positive, the line will rise as it moves from left to right.
In summary, the slope of the equation y = (3/2)x + 9 is 3/2, which describes how steep the line is and how the y value changes relative to the x value.
