The is about slope intercept form of equation is y = 3x + 66.
The straight line L's equation is given as x + 3y = 18.
Now, we can see from the attached graphic that the line crosses the x axis at point B and the y axis at position E. These are referred to as intercepts.
When y = 0, the x-intercept occurs, while the y intercept occurs 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 now have two coordinates, which are as follows:
B(18, 0) and E(0, 6)
We've been taught that AE = EB.
We can deduce from the midpoint formula that the coordinates of point E are (x + 18)/2, (y + 0)/2.
x and y are the 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
Point A's coordinates are (-18, 6).
In slope intercept form, a line's equation is y = mx + c.
Thus, y = -(1/3)x + 18 when x + 3y = 18.
where the slope is -1/3
Line M is perpendicular to line L and passes through A. As a result, the slope of line M is -1/(-1/3) = 3.
Line M's equation is y - 12 = 3(x - (-18))
⇒ y - 12 = 3x + 54
⇒ y = 3x + 66