Question

Find an equation of the line perpendicular to 9x-8y=10 that passes through the point (0,0). If possible, write the equation in slope-intercept form.

Answer 1

If we have two perpendicular lines of slopes m₁ and m₂, then we have the following equation:

`m_1\cdot m_2=-1\ldots(1)`

From the problem, we have the line with equation 9x - 8y = 10. The slope-intercept form of this line is:

`\begin{gathered} 9x-8y=10 \\ 8y=9x-10 \\ \Rightarrow y=(9)/(8)x-(5)/(4) \end{gathered}`

Then, the slope of this line is:

`m_1=(9)/(8)`

Using (1), we can find the slope of any perpendicular line to this line. Then:

`\begin{gathered} (9)/(8)\cdot m_2=-1 \\ \Rightarrow m_2=-(8)/(9) \end{gathered}`

Additionally, we know that this line passes through the point (0, 0), so the point-slope form of the perpendicular line is:

`y-0=-(8)/(9)(x-0)`

And the corresponding slope-intercept form is:

`y=-(8)/(9)x`