Question - Finding Equation of Parallel Line Passing Through a Point
Solution:
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 + 1y = -1/2 * x - 3 + 1y = -1/2 * x - 2So, 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.
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