Question

Write an equation of the line in point-slope form that passes through the given point and has the given slope. $$ (2,-1), m=3 $$

Short answer

The equation of the line in point-slope form that passes through the point (2, -1) with slope 3 is \( y + 1 = 3x - 6 \).

Step-by-step solution

Analyze and arrange data

The point given is (2,-1) so x_1 = 2 and y_1 = -1. The slope given is m = 3.

Substitute the values into the equation

We substitute the given values into the point-slope equation y - y_1 = m(x - x_1). This will give us y - (-1) = 3(x - 2).

Simplify the equation

Simplify the equation to get the final form: y + 1 = 3x - 6.