Example Question - given slope and point

Finding the Equation of a Line Given Slope and a Point

Given, slope \( m = \frac{2}{3} \) and point \( (1, -2) \). The equation of a line in slope-intercept form is \( y = mx + b \). Substituting the given slope and point into the equation to find \( b \): \( -2 = \left( \frac{2}{3} \right)(1) + b \) To solve for \( b \): \( b = -2 - \frac{2}{3} \) \( b = -\frac{6}{3} - \frac{2}{3} \) \( b = -\frac{8}{3} \) The equation of the line is: \( y = \frac{2}{3}x - \frac{8}{3} \)