Finding Equation of Parallel Line Passing Through a Point
To find the equation of line r that is parallel to line q and passes through the point (-6, 1), we start by determining the slope of line q.
The equation of line q is given in slope-intercept form as:
y = -5 - 1/2(x + 2)
In slope-intercept form, which is y = mx + b, m represents the slope and b represents the y-intercept. Based on line q's equation, the slope (m) is -1/2.
Since line r is parallel to line q, line r will have the same slope as line q. Therefore, the slope of line r will also be -1/2.
Using the point-slope form of a line equation, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line, and m is the slope, we can substitute the slope and the point through which line r passes.
The point (-6, 1) will be our (x1, y1), and our slope (m) will be -1/2.
y - y1 = m(x - x1)
y - 1 = -1/2(x - (-6))
y - 1 = -1/2(x + 6)
Now, we solve for y to get the equation in slope-intercept form.
y = -1/2 * x - 1/2 * 6 + 1
y = -1/2 * x - 3 + 1
y = -1/2 * x - 2
So, the equation of line r in slope-intercept form is:
y = -1/2x - 2
This equation uses numbers written as simplified proper fractions, improper fractions, or integers, as requested.
