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Find the equation for the line that passes through the point (-4,-3) and that is perpendicular to the line with the equation y=3/4x-1

Sagot :

Given,

The coordinate that lie on the line is (-4, -3).

The equation of line is y = 3/4x-1.

The standard equation of line is,

[tex]y=mx+c[/tex]

Here, m is the slope of the line.

On comparing, the slope of the line y = 3/4x-1 with the standard equation of line then m = 3/4.

The relation of two perpendicular line is,

[tex]\begin{gathered} m_1\times m_2=-1_{} \\ \frac{3}{4}\times m_2=-1 \\ m_2=\frac{-4}{3} \end{gathered}[/tex]

The equation of line passing through the point (-4,-3) and perpendicular to line y = 3/4x-1 is,

[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-(-3)=\frac{-4}{3}(x-(-4)) \\ y+3=\frac{-4}{3}(x+4) \\ 3y+9=-4x-16 \\ 3y=-4x-25 \\ y=\frac{-4x-25}{3} \end{gathered}[/tex]

Hence, the equation of line perpendicular to y = 3/4x-1 is y = (-4x-25)/3.