Write the equation of the line that passes through the points (7,6) and (6,-9) . Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.

To find the equation of the line that passes through the points $(7,6)$ and $(6,-9)$, we can use the point-slope form of a linear equation.<br /><br />The point-slope form of a linear equation is given by:<br />$y - y_1 = m(x - x_1)$<br /><br />where $(x_1, y_1)$ is a point on the line and $m$ is the slope of the line.<br /><br />To find the slope, we can use the formula:<br />$m = \frac{y_2 - y_1}{x_2 - x_1}$<br /><br />Substituting the given points $(7,6)$ and $(6,-9)$ into the formula, we get:<br />$m = \frac{-9 - 6}{6 - 7} = \frac{-15}{-1} = 15$<br /><br />Now that we have the slope, we can substitute one of the points and the slope into the point-slope form equation. Let's use the point $(7,6)$:<br />$y - 6 = 15(x - 7)$<br /><br />Simplifying the equation, we get:<br />$y - 6 = 15x - 105$<br />$y = 15x - 99$<br /><br />Therefore, the equation of the line that passes through the points $(7,6)$ and $(6,-9)$ is $y = 15x - 99$.