The equation of line s, which is parallel to line r and passes through the point (-2,-7), is found to be y = 3x - 1. This is determined using the slope-intercept and point-slope forms of a linear equation.
The equation of line r is y-9=3(x-10). This equation can simply be rearranged to y=3x+3(10)-9, which further simplifies to y=3x+21. The slope-intercept form of a linear equation is y=mx+b, where m is the slope and b is the y-intercept. The slope of line r is 3. Since line s is parallel to line r, it must have the same slope, which is also 3. To find the equation of line s, we use the point (-2,-7) that it passes through and its slope of 3. Applying the point-slope form of a linear equation, which is y - y1 = m(x - x1), we substitute the given point and slope into the equation to get y - (-7) = 3(x - (-2)). Simplifying this, we obtain y + 7 = 3(x + 2), and then to find the y-intercept, we expand and rearrange to the slope-intercept form to get y = 3x + 6 - 7, which simplifies further to y = 3x - 1. Thus, the equation of line s is y = 3x - 1.