Question

Draw the graph of the line that is perpendicular to Y= 4X +1 and goes through the point (2, 3)

Answer 1

Given:

$\begin{gathered} y=4x+1 \\ \text{ point }(2,3) \end{gathered}$

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:

$m_1.m_2=-1$

Slope of given line y = 4x + 1 is:

$m_2=4$

So, the slope of line perpendicular to given line is:

$m_2=-\frac{1}{4}$

Also, so line equation that is perpendicular to given line is:

$y=-\frac{1}{4}x+c...........(i)$

Also, the required line is passing thorugh given point (2, 3), i.e.,

$\begin{gathered} 3=-\frac{1}{4}(2)+c \\ c=3+\frac{1}{2} \\ c=\frac{7}{2} \end{gathered}$

So, line equation that is perpendicular to given line is:

$y=-\frac{1}{4}x+\frac{7}{2}$

The required graph of line is: