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.

Step-by-step 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=-(1)/(4)`

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

`y=-(1)/(4)x+c...........(i)`

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

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

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

`y=-(1)/(4)x+(7)/(2)`

The required graph of line is: