Line r has an equation of y=(6)/(7)x+1 . Line s includes the point (7,-7) and is ndicular to line r. What is the equation of line s? Write the equation in tercept form . Write the numbers ; in the equation as simplified proper fractions , improper fractions, or integers. square

To find the equation of line s, we need to determine its slope and then use the point-slope form of a linear equation to find the equation of the line.<br /><br />Step 1: Find the slope of line r.<br />The slope of a line can be found by looking at the coefficient of x in the equation. In this case, the slope of line r is $\frac{6}{7}$.<br /><br />Step 2: Find the slope of line s.<br />Since line s is perpendicular to line r, the slope of line s is the negative reciprocal of the slope of line r. Therefore, the slope of line s is $-\frac{7}{6}$.<br /><br />Step 3: Use the point-slope form to find the equation of line s.<br />The point-slope form of a linear equation is given by $y - y_1 = m(x - x_1)$, where $(x_1, y_1)$ is a point on the line and m is the slope.<br /><br />Using the point $(7, -7)$ and the slope $-\frac{7}{6}$, we can substitute these values into the point-slope form:<br />$y - (-7) = -\frac{7}{6}(x - 7)$<br /><br />Simplifying this equation, we get:<br />$y + 7 = -\frac{7}{6}(x - 7)$<br /><br />Step 4: Convert the equation to slope-intercept form.<br />To convert the equation to slope-intercept form, we need to solve for y:<br />$y = -\frac{7}{6}(x - 7) - 7$<br /><br />Expanding and simplifying, we get:<br />$y = -\frac{7}{6}x + \frac{49}{6} - 7$<br /><br />Combining like terms, we have:<br />$y = -\frac{7}{6}x + \frac{49}{6} - \frac{42}{6}$<br /><br />Simplifying further, we get:<br />$y = -\frac{7}{6}x + \frac{7}{6}$<br /><br />Therefore, the equation of line s in slope-intercept form is:<br />$y = -\frac{7}{6}x + \frac{7}{6}$