Question

What is the equation of the line that is perpendicular to the given line and passes through point (2,5)?

Answer 1

`\large\boxed{y=-(1)/(3)x+1}`

Explanation:

`\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\\\m-slope\\b-y-intercept\to(0,\ b)`

`\text{Let}\ k:y=m_1x+b_1\ \text{and}\ l:y=m_2x+b_2,\ \text{then}\\\\l\ \parallel\ k\iff m_1=m_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-(1)/(m_1)\\=======================\\\\\text{We must find the slope of the given line.}\\\\\text{The formula of a slope:}\\\\m=(y_2-y_1)/(x_2-x_1)\\\\\text{Substitute the coordinates of the given points from the graph (0, 1) and (-3, 2)}\\\\m_1=(2-1)/(-3-0)=(1)/(-3)=-(1)/(3)`

`\text{We have an equation:}\\\\y=-(1)/(3)x+b\\\\\text{From the coordinates of the point (0, 1) we have the y-intercept:}\ b=1.\\\\\text{Therefore we have the equation:}\\\\y=-(1)/(3)x+1`