Question

Write the equation of the line with this given information in slope intercept form

Answer 1

We have the following:

The equation of a line in its slope and y-intercept form is as follows

$y=mx+b$

where m is the slope and b is the y-intercept:

now,

When two lines are perpendicular, the product of their slopes is equal to -1

$\begin{gathered} m_1\cdot m_2=-1 \\ 3\cdot m_2=-1 \\ m_2=-\frac{1}{3} \end{gathered}$

now, for b, replacing

x = 15 and y = 2

m = -1/3

$\begin{gathered} 2=-\frac{1}{3}\cdot15+b \\ 2=-5+b \\ b=2+5 \\ b=7 \end{gathered}$

The equation is:

$y=-\frac{1}{3}x+7$