Respuesta :
The general form of the equation of a line in slope intercept is y = mx+b where m is the slope and b is the intercept. To find the equation, we simply need to find the values of m and b.
Have in mind that if we have two lines y = mx+b and y = dx+e, we say that two lines are perpendicular if the product of their slopes is -1. That is
[tex]m\cdot d\text{ = -1}[/tex]We are given the line y = (3/2)x+(1/4). For this line, the slope is (3/2). Since we want that our line y =mx+b is perpendicular to the given line, it must happen that
[tex]m\cdot(\frac{3}{2})\text{ = -1}[/tex]If we multiply by 2 on both sides and then divide by 3, we get
[tex]m\text{ = -1}\cdot\frac{2}{3}=-\frac{2}{3}[/tex]So far, we have the equation of our line to be y = (-2/3)x+b. We are given that this line passes through the point (6,1). This means that in this equation, if we replace x by 6, then we get y=1. This leads to the equation
[tex]1=(-\frac{2}{3})\cdot6+b\text{ = -2}\cdot2+b\text{ = -4+b}[/tex]So, if we add 4 on both sides, we get
[tex]b\text{ = 1+4 = 5}[/tex]So the equation of our line is y = (-2/3)*x + 5.
