through: (2,-3), slope = -3

1 answer

To find the equation of the line that passes through the point (2, -3) with a slope of -3, we can use the point-slope form of a linear equation, which is given by:

\[ y - y_1 = m(x - x_1) \]

Where:

  • \((x_1, y_1)\) is the point the line passes through (2, -3),
  • \(m\) is the slope (-3).

Substituting the values into the formula:

\[ y - (-3) = -3(x - 2) \]

This simplifies to:

\[ y + 3 = -3(x - 2) \]

Distributing the \(-3\):

\[ y + 3 = -3x + 6 \]

Now, subtracting 3 from both sides:

\[ y = -3x + 3 \]

So the equation of the line in slope-intercept form (y = mx + b) is:

\[ \boxed{y = -3x + 3} \]