lucyvickers31
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ABCD is a rectangle. A, E and B are points on the straight line L with equation x + 3y = 18. A and D are points on the straight line M. AE = EB. Find the equation for M in the form y = ax + b where a and b are integers

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quenstasiajackson

Answer:

If  B  is the  x-intercept and  E  is the  y-intercept of  x + 3y  =  18 , then

point B  =  (18, 0)       and       point E  =  (0, 6)

Then...

point A  =  (-18, 6+6)  =  (-18, 12)

Line M  is perpendicular to line L.

slope of line L  =  -6/18  =  -1/3   so..

slope of line M  =  3

So line M passes through the point  (-18, 12)  with a slope of  3 . So the equation of line M is...

y - 12  =  3(x - -18)

y - 12  =  3(x + 18)

y - 12  =  3x + 54

y  =  3x + 66

Step-by-step explanation:

This is about slope intercept form of equation.

The rectangle is missing and so i have attached it.

y = 3x + 66

  • We are told that the equation of the straight line L is x + 3y = 18

Now, from the attached image, we can see that the line crosses the x axis at point B and the y axis at point E. These points are known as intercepts.

The x-intercept is when y = 0 while the y intercept is when x = 0. Thus;

  • x-intercept;

x + 3(0) = 18

x = 18

  • y-intercept;

0 + 3y = 18

3y = 18

y = 18/3

y = 6

  • This means we have two coordinates now which are;

B(18, 0) and E(0, 6)

  • We are told that AE = EB

From midpoint formula between two points, we can say that coordinate of point E is; (x + 18)/2 , (y + 0)/2

where x and y are coordinates of point A.

Thus; (x + 18)/2 = 0

x + 18 = 0

x = -18

Also, (y + 0)/2 = 6

y + 0 = 6 × 2

y = 12

The coordinates of point A are (-18, 6)

  • The equation of a line in slope intercept form is; y = mx + c

Thus; x + 3y = 18 gives; y = -(1/3)x + 18

where -1/3 is the slope

  • Line M passes through A and perpendicular to line L. Thus slope of line M = -1/(-1/3) = 3

Equation of Line M is; y - 12 = 3(x - (-18))

⇒ y - 12 = 3x + 54

⇒ y = 3x + 66

Read more at; https://brainly.com/question/12005129

Ver imagen AFOKE88

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