The point-slope form of a linear equation is generally represented as:
y – y1 = m(x – x1)
Here, m is the slope of the line, while (x1, y1) is a point that the line passes through. In your case, the equation you provided is:
y = 3x – 2
To convert this into a linear function form, you can rewrite the equation in the slope-intercept format, which is expressed as:
y = mx + b
In this scenario:
- m (the slope) is 3
- b (the y-intercept) is -2
From the equation y = 3x – 2, you can see that the line’s slope is 3, which means that for every unit increase in x, y increases by 3 units.
The y-intercept, which is -2, tells us that the line crosses the y-axis at the point (0, -2).
So, if you are choosing a linear function based on the point-slope equation you’ve been provided, the linear function can simply be noted as:
f(x) = 3x – 2
This equation not only describes the relationship between x and y, but it also allows you to plot the line on a graph. Begin at the point (0, -2) on the y-axis and use the slope to find another point by moving up 3 units and right 1 unit. This process can be repeated to find multiple points that lie on the line. Overall, you’ve effectively crafted a straightforward linear function from the given point-slope format!