Find an equation of the line perpendicular to the graph of 14x-7=1 that passes through the point at (-2,4)

Accepted Solution

we know thatIf two lines are perpendicular, then the product o their slopes is equal to minus oneso[tex]m1*m2=-1[/tex]Step 1Find the slope of the given linewe have[tex]14x-7=1\\14x=1+7[/tex][tex]x=8/14[/tex] -------> [tex]x=4/7[/tex]This line is parallel to the y-axissothe perpendicular will be parallel to the x-axisStep 2The equation of the line perpendicular to the given line is the y-coordinate of the given pointPoint [tex](-2,4)[/tex]the equation is[tex]y=4[/tex]thereforethe answer is[tex]y=4[/tex]see the attached figure to better understand the problem