Question

write equation of the line that crosses the x-axis at 15 and is perpendicular to the line represented by y=4/9x+5

Answer 1

Since the line crosses the x-axis at 15, then

The line passes through the point (15, 0)

The line is perpendicular to the line of the equation

`y=(4)/(9)x+5`

The product of the slopes of the perpendicular lines is -1

So to find the slope of the line that perpendicular to another line,

Reciprocal the slope of the line and change its sign

If the slope of a line is m, then

The slope of its perpendicular is - 1/m

The form of the equation of a line is

y = m x + b

So the slope of the given line is 4/9

Let us find the slope of its perpendicular by reciprocal it and change its sign

The slope of the perpendicular line is -9/4

Substitute it in the form of the equation

y = -9/4 x + b

To find b substitute x and y in the equation by the coordinates of the point (15, 0)

`\begin{gathered} 0=(-9)/(4)(15)+b \\ 0=-(135)/(4)+b \end{gathered}`

Add 135/4 to both sides to find b

`\begin{gathered} 0+(135)/(4)=-(135)/(4)+(135)/(4)+b \\ (135)/(4)=b \end{gathered}`

Substitute it in the equation

`y=-(9)/(4)x+(135)/(4)`