Given:
A line passes through (1,-2) and is perpendicular to [tex]-4x+7y=21[/tex].
To find:
The equation of that line.
Solution:
We have, equation of perpendicular line.
[tex]-4x+7y=21[/tex]
Slope of this line is
[tex]m_1=-\dfrac{\text{Coefficient of x}}{\text{Coefficient of y}}[/tex]
[tex]m_1=-\dfrac{-4}{7}[/tex]
[tex]m_1=\dfrac{4}{7}[/tex]
Product of slope of two perpendicular lines is -1.
[tex]m_1\times m_2=-1[/tex]
[tex]\dfrac{4}{7}\times m_2=-1[/tex]
[tex]m_2=-\dfrac{7}{4}[/tex]
Now, slope of required line is [tex]-\dfrac{7}{4}[/tex] and it passes through (1,-2). So, the equation of line is
[tex]y-y_1=m(x-x_1)[/tex]
where, m is slope.
[tex]y-(-2)=-\dfrac{7}{4}(x-1)[/tex]
[tex]4(y+2)=-7(x-1)[/tex]
[tex]4y+8=-7x+7[/tex]
[tex]4y+7x=7-8[/tex]
[tex]7x+4y=-1[/tex]
Therefore, the equation of required line is [tex]7x+4y=-1[/tex].
