Question

Write the equation of the line passing through point (-3,3) and perpendicular to y=x + 3

Answer 1

Two lines are perpendicular to each other when the product between their slopes is equal to -1.

`y=x+3`

Then, we can write the following equation to find the missing slope

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

since we have the slope for the initial line we can leave only one unknown variable, and clear the equation

`\begin{gathered} (1)\cdot(m_2)=-1 \\ m_2=-1 \end{gathered}`

then using the point given and the standard form of the equation of the line find the y-intercept

`\begin{gathered} y=mx+b \\ \text{point (-3,3)} \\ y=-x+b \\ 3=-(-3)+b \\ 3=3+b \\ b=3-3 \\ b=0 \end{gathered}`

the equation of the line is

`y=-x`