Question

5Find the equation of the line through (-2, 2) andperpendicular to the line y = x - 5. Put inуslope-intercept form.1=3-

Answer 1

The slope-intercept form of a line is:

y = mx + b

Where m is the slope and b is the y-intercept.

Two lines having slopes m1 and m2 are perpendicular if

m1 * m2 = -1

We are given the equation of one line:

`y=(1)/(3)x-5`

It's required to find the equation of another line that is perpendicular to it. We have m1 = 1/3, let's find the other slope:

`\begin{gathered} m_1\cdot m_2=-1 \\ (1)/(3)\cdot m_2=-1 \\ Thus\colon \\ m_2=-3 \end{gathered}`

The slope of the required line is -3. Now we use the point through which the line passes (-2, 2).

We use the point-slope form of the line:

y - k = m( x - h)

Where (h,k) = (-2, 2) is the point. Substituting:

`y-2=-3(x+2)`

Operating:

`\begin{gathered} y-2=-3x-6 \\ \text{Adding 2:} \\ \boxed{y=-3x-4^{}} \end{gathered}`