Respuesta :
We have the next given equation:
[tex]2x+y=3[/tex]a) The slope-intercept form is given by the next form:
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept
To get this form, we need to solve for y the equation:
[tex]2x+y=3[/tex][tex]y=-2x+3[/tex]b) When two lines parallel, they have the same slope. Therefore the slope is -2.
c) When two lines are perpendicular to each other the multiplication of both slopes is equal to -1.
The slope is
-2* m = -1
m= -1/ -2
m= 1/2
d)
We have that the line perpendicular to the line must have a slope equal to 1/2.
Then, we can use the next slope-intercept form to get the equation line:
[tex]y-y_1=m(x-x_1)[/tex]where m= 1/2 and P1(x1, y1) = (5,4)
Replacing the values:
[tex]y-4=\frac{1}{2}(x-5)[/tex][tex]y-4=\frac{1}{2}x-\frac{5}{2}[/tex]Solving for y =
[tex]y=\frac{1}{2}x-\frac{5}{2}+4^{}[/tex][tex]y=\frac{1}{2}x+\frac{3}{2}[/tex]