Question

A line parallel to x − 2y − 4 = 0 crosses the negative x axis and positive y axis so that the line and these axes form a right triangle of area 9. whats the equation of the line?

Answer 1

Answer: y=0.5x+3 or 0.5x+3-y=0

Note: The lines are parallel if their slope are equal

Step-by-step explanation:

First we rearrange the equation

x-2y-4=0 to y=(x-4)÷2 let this be a function f(x)

so f(x)=(x-4)÷2 then we choose two points to find the slope of this function,

f(4)=(4-4)÷2=0, f(2)=(2-4)÷2=-1

we got (4;0) and (2;-1)

Next, slope=(0-(-1) )÷(4-2)=0.5

From here we going to use this for the unknown line, given the line forms a right triangle whose area is 9 we can think of the possible values

so a right triangle area's formula is

0.5×base×height=9,

well it's easy to guess that the solution is 18

I simplify 18 into 3×3×2 to narrow possible choices for x and y:

6×3 or 9×2

here I'm going to skip a detail and jump to the answer

so x is -6 and y is 3 to get the equation we use point-intercept form

y-y{sub zero}=slope(x -x{sub zero}), Remainder the slope 0.5 then I choose the point (-6;0) and put into the formula above

y-0=0.5(x-(-6)) thus y=0.5x+3 or 0.5x+3-y=0