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 + 3(0) = 18
x = 18
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)
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
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