To convert the equation of the line from slope-intercept form (y = mx + b) to standard form (Ax + By = C), we start with the given equation:
y = 3x + 10
Here, ‘m’ is the slope (3) and ‘b’ is the y-intercept (10). The goal is to rearrange this equation so that it fits the standard form.
To do this, we need to move the terms involving ‘x’ and ‘y’ to one side of the equation. We can start by subtracting 3x from both sides:
y – 3x = 10
Next, let’s rearrange it to match the standard format:
-3x + y = 10
Now, we usually want the ‘A’ value to be positive in standard form. To achieve this, we can multiply all terms by -1:
3x – y = -10
Thus, the standard form of the equation of the line is:
3x – y = -10