To write the equation of a line passing through the point (3, -5), we generally start with the point-slope form of the equation of a line. This form is:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
Here, [tex]\( (x_1, y_1) \)[/tex] represents a point through which the line passes, and [tex]\( m \)[/tex] represents the slope of the line. In this case, we know that the line passes through the point [tex]\( (3, -5) \)[/tex]. Therefore, we can substitute [tex]\( x_1 = 3 \)[/tex] and [tex]\( y_1 = -5 \)[/tex] into the equation.
Substituting these values into the point-slope form, we get:
[tex]\[ y - (-5) = m(x - 3) \][/tex]
This simplifies to:
[tex]\[ y + 5 = m(x - 3) \][/tex]
To express the equation in a more standard form, we isolate [tex]\( y \)[/tex]:
[tex]\[ y = m(x - 3) - 5 \][/tex]
Therefore, the equation of a line passing through the point [tex]\( (3, -5) \)[/tex] in terms of slope [tex]\( m \)[/tex] is:
[tex]\[ y = m(x - 3) - 5 \][/tex]
If you know the specific value of the slope [tex]\( m \)[/tex], you can substitute it into the equation to get the specific line equation. Without a specific slope, the final form remains in terms of [tex]\( m \)[/tex]:
[tex]\[ y = m(x - 3) - 5 \][/tex]
