Respuesta :
Answer:
[tex]y - 3 = \frac{1}{4}(x+2)[/tex] or choose any line with slope 1/4
Step-by-step explanation:
The slope of this line is -4. The slope of the line perpendicular to this line will be the negative reciprocal or 1/4.
Write the equation using the slope m=1/4 and the point slope form.
[tex]y-y_1=m(x-x_1)\\y-3=\frac{1}{4}(x+2)[/tex]
This is the equation of the line that is perpendicular and passes through the same point (-2,3) as the equation listed.
Answer:
[tex]y=\frac{1}{4} x+c[/tex] where [tex]c[/tex] can be any number.
Step-by-step explanation:
First we need to clear for y:
[tex]y-3 =-4(x+2)\\y=-4(x+2)+3\\y=-4x-8+3\\y=-4x-5[/tex]
and now we have an equation of the form:
[tex]y=mx+b[/tex]
where m is the slope and b is the y-intercept.
in this case [tex]m=-4[/tex] and [tex]b=-5[/tex]
to find and equation perpendicular to this line, the following must be true:[tex]m*m_{1}=-1[/tex]
where m is the slope of the original line that i just mentioned, and [tex]m_{1}[/tex] is the slope of the new line. Substituting [tex]m=-4[/tex]
[tex]-4*m_{1}=-1[/tex]
clearing for [tex]m_{1}[/tex]
[tex]m_{1}=\frac{-1}{-4} \\m_{1}=\frac{1}{4}[/tex]
thus, the new perpendicular line must have the form:
[tex]y=m_{1}x+c\\y=\frac{1}{4}x+c[/tex]
where the y-intecept [tex]c[/tex] can be any number, some examples are:
[tex]y=\frac{1}{4}x+3\\y=\frac{1}{4}x-8[/tex]
and so on, the important thing to be a perpendicular line is that the slopes are related to the equation [tex]m*m_{1}=-1[/tex].
