Question

Find the equation of a line perpendicular to the given line and pass through the given point. Write equation in slope-intercept form Line y= -4/5x + 2 point, (8,9) Graph

Answer 1

Equation:

`y=(5)/(4)x-1`

Graph:

The red line is the graph of the given line and the green line is the graph of the perpendicular line passing through (8, 9).

Step-by-step explanation

The equation of the line is given in the slope-intercept form,

`y=-(4)/(5)x+2`

The slope is -4/5 and the y-intercept is 2.

Two lines are perpendicular if their slopes are opposite reciprocals of each other. Therefore, a perpendicular line to the given line has a slope of 5/4,

`y=(5)/(4)x+b`

There is an infinite number of perpendicular lines, but there is only one that passes through the point (8, 9). Replace x and y with the coordinates of this point in the equation above,

`9=(5)/(4)\cdot8+b`

And solve for b,

`\begin{gathered} 9=5\cdot2+b \\ 9=10+b \\ 9-10=b \\ -1=b \end{gathered}`

Hence, the equation of the perpendicular line is,

`y=(5)/(4)x-1`