Point(-7, 1)Linex + y = 2Exercise (a)Write an equation of the line through the point parallel to the given line.Step 1Two 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 isy = 2-xThe slope of this line isStep 2The 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 -1y - 1 =XStep 3Simplify and write the final equation in general form.y − 1 = −1(x − (−7))The equation of the parallel line is= 0Submit Skip (you cannot come back)m =-x+2The negative reciprocal of -1 is1Exercise (b)Write an equation of the line through the point perpendicular to the given line.-1 (xStep 1Two 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 ))

(-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).