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
[tex]y=\frac{4}{9}x+5[/tex]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)
[tex]\begin{gathered} 0=\frac{-9}{4}(15)+b \\ 0=-\frac{135}{4}+b \end{gathered}[/tex]Add 135/4 to both sides to find b
[tex]\begin{gathered} 0+\frac{135}{4}=-\frac{135}{4}+\frac{135}{4}+b \\ \frac{135}{4}=b \end{gathered}[/tex]Substitute it in the equation
[tex]y=-\frac{9}{4}x+\frac{135}{4}[/tex]