Given:
[tex]\begin{gathered} y=4x+1 \\ \text{ point }(2,3) \end{gathered}[/tex]
To find:
Draw a graph of a line that is perpendicular to the given line and passing through a given point.
Explanation:
As we know that relation between two slopes of perpendicular slopes of lines:
[tex]m_1.m_2=-1[/tex]
Slope of given line y = 4x + 1 is:
[tex]m_2=4[/tex]
So, the slope of line perpendicular to given line is:
[tex]m_2=-\frac{1}{4}[/tex]
Also, so line equation that is perpendicular to given line is:
[tex]y=-\frac{1}{4}x+c...........(i)[/tex]
Also, the required line is passing thorugh given point (2, 3), i.e.,
[tex]\begin{gathered} 3=-\frac{1}{4}(2)+c \\ c=3+\frac{1}{2} \\ c=\frac{7}{2} \end{gathered}[/tex]
So, line equation that is perpendicular to given line is:
[tex]y=-\frac{1}{4}x+\frac{7}{2}[/tex]
The required graph of line is:
