Question - Finding the Equation of a Line Given Slope and a Point
Solution:
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:$$ y = \frac{2}{3}x - \frac{8}{3} $$
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