The equation of a line that is perpendicular to the given line is y = -4/3x + c.
The equation of a line means an equation in x and y whose solution set is a line in the (x,y) plane. The standard form of equation of a line is ax + by + c = 0. Here a, b, are the coefficients, x, y are the variables, and c is the constant term.
For the given situation,
The equation of a line is y = 3/4x - 1/2 ------ (1)
The general form of equation of line in slope intercept form is
[tex]y=mx+c[/tex]
On comparing the equation 1 with general form,
Slope of the line, [tex]m=\frac{3}{4}[/tex]
Then, the slope of the line perpendicular to the given line is [tex]\frac{-1}{m}[/tex]
⇒ [tex]\frac{-1}{m}=\frac{-1}{\frac{3}{4} }[/tex]
⇒ [tex]\frac{-1}{m}=\frac{-4}{3}[/tex]
No points were defined that this 'normal' should pass through, so its intercepts are indeterminate.
Thus the equation of line in slope intercept form is
[tex]y=\frac{-4}{3}x+c[/tex]
Hence we can conclude that the equation of a line that is perpendicular to the given line is y = -4/3x + c.
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