The point-slope equation that you provided is y = 3x + 5. To clarify how we derive the linear function from this point-slope form, let’s break it down step by step.
The point-slope form of a linear equation is generally expressed as:
y – y1 = m(x – x1)
In this equation:
– m represents the slope of the line
–
(x1, y1) is a specific point on the line
In your case, it seems like you might have meant to write the equation another way. In the form y – y1 = m(x – x1), if we consider y = 3x + 5 to be in slope-intercept format, it can be interpreted as:
- Slope (m): 3
- y-intercept: 5 (the point where the line crosses the y-axis)
This means that for every unit increase in x, the value of y increases by 3 units. Additionally, when x is 0, y will be 5, indicating that the line crosses the y-axis at the point (0, 5).
In conclusion, the linear function representing the line from the point-slope equation you’ve provided can be succinctly stated as y = 3x + 5. This linear equation is easily recognizable and depicts a straight line with a consistent slope.