Answer:
Therefore, the equation of line s is y = 3x - 1.
Explanation:
To find the equation of line s, which is parallel to line r, we need to determine the slope of line r and then use that slope to write the equation of line s.
1. The equation of line r is given as y - 9 = 3(x - 10). This equation is in slope-intercept form (y = mx + b), where m is the slope of the line.
2. By comparing the equation of line r with the slope-intercept form, we can see that the slope of line r is 3.
3. Since line s is parallel to line r, it will have the same slope. Therefore, the slope of line s is also 3.
4. We also know that line s includes the point (-2, -7). Using this point and the slope of 3, we can write the equation of line s using the point-slope form (y - y1 = m(x - x1)).
Let's substitute the values into the point-slope form:
y - (-7) = 3(x - (-2))
y + 7 = 3(x + 2)
5. Simplify the equation by distributing the 3 on the right side:
y + 7 = 3x + 6
6. Finally, rearrange the equation to get it in slope-intercept form:
y = 3x + 6 - 7
y = 3x - 1