Respuesta :
The general form for the equation of a line is:
[tex]y = mx + c[/tex]
Where:
m is the gradient of the line
c is the y intercept of the line (y - intercept is where the graph crosses the y-axis)
So if you had the following equation:
[tex]y = 3x + 2[/tex]
Then:
m = 3
c = 2
So gradient = 3, and y intercept = 2
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Rearranging
So first rearrange both of the equations in the form y = mx + c :
[tex]3x + 2y = -1[/tex] becomes [tex]y = -\frac{3}{2} x-\frac{1}{2}[/tex] [tex](where: \ m = -\frac{3}{2} \ and, \ c = -\frac{1}{2} )[/tex]
and:
[tex]2x+7y=2[/tex] becomes [tex]y=-\frac{2}{7}x +\frac{2}{7}[/tex] [tex](where: \ m = -\frac{2}{7} \ and, \ c = \frac{2}{7})[/tex]
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The question tells us that the equation of the line we are looking for has the same y-intercept as:
[tex]2x+7y=2[/tex]
So the line we are trying to work out will also have a y intercept of [tex]\frac{2}{7}[/tex]
(refer to rearranging)
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The question also tells us that the line is perpendicular to [tex]3x + 2y = -1[/tex]
Perpendicular gradient = negative reciprocal of the gradient of the line it is perpendicular to.
So the gradient of the new line will be the negative reciprocal of the gradient of [tex]3x + 2y = -1[/tex]
Gradient of [tex]3x + 2y = -1[/tex] is: [tex]-\frac{3}{2}[/tex]
(refer to rearranging)
Gradient of new line: = negative reciprocal of [tex]-\frac{3}{2}[/tex] , which is [tex]\frac{2}{3}[/tex]
(just flip fraction and change the sign)
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So for the new line: [tex]m = \frac{2}{3} \ and, \ c = \frac{2}{7}[/tex]
So just substitute in the values for m and c into: y = mx + c
[tex]y = mx + c\\y = \frac{2}{3} x + \frac{2}{7}[/tex]
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Answer:
So equation of the new line is:
[tex]y = \frac{2}{3}x + \frac{2}{7}[/tex]
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Any questions, just ask.
