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Write an equation of the line tht passes through the given point and is perpendicular to the graph of the given equation?

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4 Answers

Let's take a look at the frist problem. 2 and 3 can be solved the same way.

First of all you have to rewrite your equation 3x + y = 5 (this is a standard form) in slope-intercept form by subtracting 3x from both sides of the equation. We have y = -3x +5. That means the sloppe of the line is

m=-3 (if we use y = mx+b form of the linear equation). The line which is perpendicular to that will have the slope equal to the reciprocal of (-3) taken with negative sign. Thus, the  new slope equals 1/3. Or your equation for the perpendicular line should be like

                                                           y = (1/3)x +b

In order to find "b" use the point given in the problem. If x =-9 y =3. Thus, we have

                                   3 = (1/3)(-9) +b = -3 +b        or b = 3+3 =6

The equation for  a perpendicular line becomes

                                            y = (1/3)x +6

Repeat the same steps for problems 2 and 3.

1. The equation can be rewritten y = 5 - 3x, which is in slope-intercept form. This makes it obvious that the slope of the line is -3. To find the slope of a line perpendicular to it, you take the negative reciprocal of the known slope. -(-3)^(-1) = 1/3 which is the slope we desire. We can write a new equation in point slope form: y - y0 = m(x-x0) where (x0, y0) is a point on the line. Substituting the point given and the slope 1/3, we get y + 3 = (x - -9)/3 = (x+9)/3. Adding three to both sides: y = (x + 9)/3 + 9/3 = (x + 9 + 9)/3 = (x + 18)/3. So the equation we seek is y = (x + 18)/3 or y= x/3 + 6

2.The slope is -2/3, so the slope of our new line will be 3/2. It has to pass through (-8,3) so y-3 = 3(x+8)/2 or y = 3(x+10)/2

3. The slope is -1, so the slope of our new line will be 1. It has to pass through (3,-6) so y+6=(x-3) or y = x - 9


1. You can just switch the numbers in front of x and y and make one of them negative. i.e. instead of the original equation 3x+1y=5 write 1x-3y=...  Then for the Right hand side of the equation, write the same thing as the Left hand side but replace the x with -9 and y with 3 to get

1x-3y=1(-9)-3(3)=-9-9=-18. That is x-3y=-18 is the answer.

2. For question 2, you have to rewrite it in the form of question 1 in order to use this method. this will be 2x+3y=-8. so write

3x-2y=3(-3)-2(3)=-9-6=-15 so 3x-2y=-15 is your answer.

3. This is similar to the form of question 1. Instead of 1x+1y=-4 write

1x-1y=1(3)-1(-6) =3+6=9 so you have x-y=9 as answer.