Question

You are given the line whose equation is 2x + y = 3. Answer the following questions:a)Write the given equation in slope-intercept formb)What is the slope of the line parallel to this linec)What is the slope of the line perpendicular to this lined) What is the equation of the line that passes through the point(5,4) and is perpendicular to the line whose equation is 2x + y = 3 in slope intercept form.

Answer 1

We have the next given equation:

`2x+y=3`

a) The slope-intercept form is given by the next form:

`y=mx+b`

Where m is the slope and b is the y-intercept

To get this form, we need to solve for y the equation:

`2x+y=3`
`y=-2x+3`

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:

`y-y_1=m(x-x_1)`

where m= 1/2 and P1(x1, y1) = (5,4)

Replacing the values:

`y-4=(1)/(2)(x-5)`
`y-4=(1)/(2)x-(5)/(2)`

Solving for y =

`y=(1)/(2)x-(5)/(2)+4^{}`
`y=(1)/(2)x+(3)/(2)`