Question

write an equation in slope intercept form for the line that passes through the given point and is perpendicular to the graph of the equation. (-4,2); y= -1/2x + 6

Answer 1

First of all we are going to find the slope perpendicular to the equation y = -1/2 x +6.

We need to remember that two slopes are perpendicular if its product is equal to -1. Like this:

$\begin{gathered} m_1\cdot m_2=-1 \\ m_1=-\frac{1}{2}_{} \\ m_2=-\frac{1}{m_1}=-\frac{1}{-\frac{1}{2}}=2 \\ m_2=2 \end{gathered}$

Now, we find the equation of the line using the general form:

$(y-y_1)=m(x-x_1);\text{ }$

m - slope

$(x_1,y1)=(-4,2)_{}$

That was a point of the line, now:

$\begin{gathered} (y-2)=2(x-(-4)) \\ y-2=2x+8 \\ y=2x+10 \end{gathered}$

Finally, the equation of the line that passes through (-4,2) and is perpendicular to the equation y = -1/2x+6 is

y=2x+10