contestada

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

What is the equation of the line that is perpendicular to the given line and passes through point 25 class=

Respuesta :

gmany

Answer:

[tex]\large\boxed{y=-\dfrac{1}{3}x+1}[/tex]

Step-by-step explanation:

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

[tex]\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=-\dfrac{1}{m_1}\\=======================\\\\\text{We must find the slope of the given line.}\\\\\text{The formula of a slope:}\\\\m=\dfrac{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=\dfrac{2-1}{-3-0}=\dfrac{1}{-3}=-\dfrac{1}{3}[/tex]

[tex]\text{We have an equation:}\\\\y=-\dfrac{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=-\dfrac{1}{3}x+1[/tex]