Question

A line passes through (3, 7) and (6, 9). Which equation best represents the line? (4 points)

Answer 1

$\text{The slope-intercept form: }y=mx+b\\\text{The point-slope form: }y-y_1=m(x-x_1)\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\-------------------------------\\\text{We have the points}\ (3,\ 7)\ \text{and}\ (6,\ 9).\ \text{Substitute:}\\\\m=\dfrac{9-7}{6-3}=\dfrac{2}{3}\\\\y-7=\dfrac{2}{3}(x-3)\qquad|\text{use distributive property}\\\\y-7=\dfrac{2}{3}x-2\qquad|+7\\\\\boxed{y=\dfrac{2}{3}x+5}$