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(-7, 1) x+y=2 Exercise (a) Write an equation of the line through the point parallel to the given line. Step 1 Two distinct non-vertical lines are parallel when their slopes are equal. Since the required line is parallel to the line x + y = 2, the slope of the required line is equal to the slope of the line x + y = 2. Begin by finding the slope of this line. The slope-intercept form of the linear equation x+y= 2 is y= 2 - x The slope of this line is -1 Step 2 The required line passes through (-7, 1). Substitute the values (x₁, y₁)= (-7, 1) and m = -1 into the point-slope form of an equation. y-y₁ = m(x-x₂) 1 - 1x 2-1 (x-(-7✔-7 >> y -1+2 Step 3 Simplify and write the final equation in general form. y-1 = -1(x-(-7)) y-1 = = 0 The equation of the parallel line is Submit Skip (you cannot come back) Exercise (b) Write an equation of the line through the point perpendicular to the given line. Step 1 Two distinct non-vertical lines are perpendicular when their slopes are negative reciprocals of each other. The slope of the required line is equal to the negative reciprocal of the slope of the line x + y = 2 which was found to be -1 in part (a).

(-7, 1) x+y=2 Exercise (a) Write an equation of the line through the point parallel to the given line. Step 1 Two distinct non-vertical lines are parallel when their slopes are equal. Since the required line is parallel to the line x + y = 2, the slope of the required line is equal to the slope of the line x + y = 2. Begin by finding the slope of this line. The slope-intercept form of the linear equation x+y= 2 is y= 2 - x The slope of this line is -1 Step 2 The required line passes through (-7, 1). Substitute the values (x₁, y₁)= (-7, 1) and m = -1 into the point-slope form of an equation. y-y₁ = m(x-x₂) 1 - 1x 2-1 (x-(-7✔-7 >> y -1+2 Step 3 Simplify and write the final equation in general form. y-1 = -1(x-(-7)) y-1 = = 0 The equation of the parallel line is Submit Skip (you cannot come back) Exercise (b) Write an equation of the line through the point perpendicular to the given line. Step 1 Two distinct non-vertical lines are perpendicular when their slopes are negative reciprocals of each other. The slope of the required line is equal to the negative reciprocal of the slope of the line x + y = 2 which was found to be -1 in part (a).

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Point (-7, 1) Line x + y = 2 Exercise (a) Write an equation of the line through the point parallel to the given line. Step 1 Two distinct non-vertical lines are parallel when their slopes are equal. Since the required line is parallel to the line x + y = 2, the slope of the required line is equal to the slope of the line x + y = 2. Begin by finding the slope of this line. The slope-intercept form of the linear equation x + y = 2 is y = 2-x The slope of this line is Step 2 The required line passes through (-7, 1). Substitute the values (X₁, Y₁) = (−7, 1) and m = −1 into the point-slope form of an equation. y - y₁ = m(x -x₁) y - 1 y - 1 = X Step 3 Simplify and write the final equation in general form. y − 1 = −1(x − (−7)) The equation of the parallel line is = 0 Submit Skip (you cannot come back) m = -x+2 The negative reciprocal of -1 is 1 Exercise (b) Write an equation of the line through the point perpendicular to the given line. -1 (x Step 1 Two distinct non-vertical lines are perpendicular when their slopes are negative reciprocals of each other. The slope of the required line is equal to the negative reciprocal of the slope of the line x + y = 2 which was found to be -1 in part (a). = -7 ))
Transcribed Image Text:Point (-7, 1) Line x + y = 2 Exercise (a) Write an equation of the line through the point parallel to the given line. Step 1 Two distinct non-vertical lines are parallel when their slopes are equal. Since the required line is parallel to the line x + y = 2, the slope of the required line is equal to the slope of the line x + y = 2. Begin by finding the slope of this line. The slope-intercept form of the linear equation x + y = 2 is y = 2-x The slope of this line is Step 2 The required line passes through (-7, 1). Substitute the values (X₁, Y₁) = (−7, 1) and m = −1 into the point-slope form of an equation. y - y₁ = m(x -x₁) y - 1 y - 1 = X Step 3 Simplify and write the final equation in general form. y − 1 = −1(x − (−7)) The equation of the parallel line is = 0 Submit Skip (you cannot come back) m = -x+2 The negative reciprocal of -1 is 1 Exercise (b) Write an equation of the line through the point perpendicular to the given line. -1 (x Step 1 Two distinct non-vertical lines are perpendicular when their slopes are negative reciprocals of each other. The slope of the required line is equal to the negative reciprocal of the slope of the line x + y = 2 which was found to be -1 in part (a). = -7 ))
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