Which of the following is the equation of a straight line that has y-intercept 3 and is perpendicular to the line 4x - 2y = 6. A.) 2y + 3x = - 3 B.) y + 3x = -2 C.) 2y - x = 6 D.) y - 2x = 4 E.) 2y + x = 6 To find the y-intercept, get each possible answer in slope-intercept formy = mx + b m is the slope b is the y-intercept Also, perpendicular lines have slopes which are negative reciprocals. For example 3/2 and -2/3 are negative reciprocals. Once, the possible answers are in slope-intercept form, you can look at the slope and y-intercept, to decide which one is being asked for.The given equation in the problem: 4x - 2y = 6 -2y = -4x + 6 {subtracted 4x from both sides} y = 2x - 3 {divided both sides by -2} slope = 2 and y-intercept = -3 a perpendicular line to this would have a slope of -1/2 So, out of the possible answers, you are looking for a slope of -1/2 and a y-intercept of 3 A.) 2y + 3x = - 3 2y = -3x - 3 {subtracted 3x from both sides} y = (-3/2)x - 3/2 {divided both sides by 2} slope = -3/2 and y-intercept = -3/2 B.) y + 3x = -2 y = -3x - 2 {subtracted 3x from both sides} slope = -3 and y-intercept = -2 C.) 2y - x = 6 2y = x + 6 {added x to both sides} y = (1/2)x + 3 {divided both sides by 2} slope = 1/2 and y-intercept = 3 D.) y - 2x = 4y = 2x + 4 {added 2x to both sides} slope = 2 and y-intercept = 4 E.) 2y + x = 6 2y = -x + 6 {subtracted x from both sides} y = (-1/2)x + 3 {divided both sides by 2} slope = -1/2 and y-intercept = 3 The line with a slope of 3 and perpendicular to 4x - 2y = 6 is E.) 2y + x = 6- Algebra House
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