Question

What is the equation of a line that is perpendicular to the equation y = {x and goes through the point (-4, 7)?

Answer 1

If two lines ar perpendicular their slopes satisfy the following equation:

`m_1=-(1)/(m_2)`

For line y=x the slope m1=1, so the slope m2 for the line we are finding is:

`\begin{gathered} m_1=1 \\ m_1=-(1)/(m_2)\Rightarrow m_2=-\frac{1}{m_1_{}}=-1 \end{gathered}`

We know the slope is m2 = -1, now the line pass through the point (-4,7), so the point 9-4,7) satisfy the equation of the line:

`\begin{gathered} y=m_2\cdot x+b \\ We\text{ use the point (x,y)=(-4,7) and the slope=-1:} \\ 7=-1\cdot(-4)+b \\ 7=4+b\Rightarrow b=7-4=3 \end{gathered}`

So, the equation of the line is:

`y=-x+3`