Question

Write an equation of the line that is perpendicular to the line y = 1 2 x + 8 that passes through the point (4,6)

Answer 1

B) y = -2x + 14

Explanation:

Solution: y = -2x + 14. To solve this problem, first determine the slope of your line. Since perpendicular lines have slopes that are opposite reciprocals of each other, we know that the slope is -2. Then plug your slope (-2) and point (4,6) into the equation y = mx + b to solve for b. The resulting value for b is 14.

Answer 2

`\large\boxed{y=-2x+14}`

Explanation:

`\text{Let}\ k:y=_1x+b_1\ \text{and}\ l:y=m_2x+b_2.\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-(1)/(m_1)\\============================\\\\\text{We have}\ y=(1)/(2)x+8\to m_1=(1)/(2).\\\\\text{Therefore}\ m_2=-(1)/((1)/(2))=-2.\\\\\text{The equation of the searched line:}\ y=-2x+b.\\\\\text{The line passes through }(4,\ 6).`

`\text{Put thecoordinates of the point to the equation.}\ x=4,\ y=6:`

`6=-2(4)+b\\\\6=-8+b\qquad\text{add 8 to both sides}\\\\b=14`