"Q: Find the equation of the line parallel to the line 3x+7y+42=0 and four units above it." What does "four units above it" mean? Also a similar question has "three units from it" What does it mean? I know how to solve such problems but I am stuck with this linguistic problem.
2007-09-02 14:17:24 · 3 answers · asked by Legend 3 in Science & Mathematics ➔ Mathematics
above it means up the y axis
3x + 7y + 42 = 0
7y = -3x - 42
y = -3/7(x) - 6
the y intercept is -6
4 units up is -2
a parrallel line would be, y = -3/7(x) -2
3 units from it would be from where it crosses the x axis
3x + 7y + 42 = 0
3x = - 7y - 42
x = -7/3(y) - 14
the x intercept = -14. 3 units from it would be, -11
y = -3/7(x) - 11 also parrallel
2007-09-02 14:28:40 · answer #1 · answered by Anonymous · 1⤊ 0⤋
3x + 7y + 42 = 0 has a slope of -3/7 and a y-intercept of -6. A line parallel and four units above it would have a slope of -3/7 and a y-intercept of -2. Equation would be y = -3/7 x - 2 or
3x + 7y + 14 = 0. The equation "three units from it" would have 2 solutions; a parallel line on either side. Those 2 lines would have a slope of -3/7. The points that are 3 units from the line would lie on the circle x^2 + (y+6)^2 = 9. The line perpendicular to the given line going through (0,-6) is y = 7/3 x - 6. This circle and perpendicular line will intersect in 2 points, each of which are 3 units from the given line. You have the slope (-3/7) and can determine these 2 points and determine the equations of the 2 lines that are 3 units from it.
2007-09-02 21:48:26 · answer #2 · answered by Marvin 4 · 0⤊ 0⤋
I would take "four units above it" to mean the vertical distance between the two lines. I would take "three units from it" to mean the perpendicular distance between the two lines.
Since you said you know how to solve such problems, I'll leave the rest to you.
2007-09-02 21:27:30 · answer #3 · answered by Northstar 7 · 0⤊ 0⤋