Answer:
Equation of line s (in point-slope form): y + 1 = -3/2(x + 1)
Explanation:
Relationship between the slopes of parallel lines:
- The slopes of parallel lines are equal to each other.
- This means that finding the slope of line r will also allow us to find the slope of line s.
Form of line r and how to convert it to slope-intercept form to find its slope:
The equation for line r is in the point-slope form of a line, whose general equation is given by:
y - y1 = m(x - x1), where
- (x1, y1) is one point on the line,
- and m is the slope is the slope.
We can easily find the slope of line r by converting it from point-slope form to slope-intercept form, whose general equation is given by:
y = mx + b, where
- m is the slope,
- and b is the y-intercept.
Thus, we can use the following steps to convert line r to slope-intercept form:
Step 1: Distribute -3/2 on the right-hand side:
y + 6 = (-3/2 * x) + (-3/2 * 6)
y + 6 = -3/2x -18/2
y + 6 = -3/2x - 9
Step 2: Subtract 6 from both sides to convert line r to slope-intercept form:
(y + 6 = -3/2x - 9) - 6
y = -3/2x - 15
Thus, the slope of line r and line s is -3/2.
Writing the equation of line s in point-slope form:
Now we can find the equation of line s in point-slope form by substituting -3/2 for m and (-1, -1) for (x1, y1):
y - (-1) = -3/2(x - (-1))
y + 1 = -3/2(x + 1)
Therefore, given that lines r and s are parallel, y + 1 = -3/2(x + 1) is the equation of line s, which passes through the point (-1, -1).