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Jan. 29, 2023•0 likes•2 views

Jan. 29, 2023•0 likes•2 views

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Write an equation of the line containing the given point and parallel to the given line. (3, 4); x+2y = 7 Express your answer in the form y=mx+b. Solution First, you know that parallel lines have the same slope. Second, get the given equation into slope-intercept form. x +2y = 3 2y = -x +3 y = -x/2 +3/2 So, the slope = -1/2. The y-intercept = 3 The x-intercept is where y=0, so that\'s x=3. A graph is useful. . But that line does not go through (7,9). . So, we have to find the value for b that will shift the line up or down to go through (7,9). 9 = -1/2*7 + b Multiply though by 2 18 = -7 + 2b 25 = 2b 2b = 25 b = 25/2 which means the equation is y = -x/2 + 25/2 Again, a graph is useful. .

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- 1. Write an equation of the line containing the given point and parallel to the given line. (3, 4); x+2y = 7 Express your answer in the form y=mx+b. Solution First, you know that parallel lines have the same slope. Second, get the given equation into slope-intercept form. x +2y = 3 2y = -x +3 y = -x/2 +3/2 So, the slope = -1/2. The y-intercept = 3 The x-intercept is where y=0, so that's x=3. A graph is useful. . But that line does not go through (7,9). . So, we have to find the value for b that will shift the line up or down to go through (7,9). 9 = -1/2*7 + b Multiply though by 2 18 = -7 + 2b 25 = 2b 2b = 25 b = 25/2 which means the equation is y = -x/2 + 25/2 Again, a graph is useful.