Question

Write the slope-intercept form of the equation of the line described.

7) through: (4,0), parallel to y=-x+ 2

8) through: (4,3), perp. to y=-*-1
9

Answer 1

7)

Given the line

`y=-x+2`

We know that the slope-intercept form of the line equation is

`y=mx+b`

here

m is the slope and b is the intercept

Thus, the slope = -1

We know that the parallel lines have the same. Thus, the slope of the parallel line is: -1

Using point-slope of the line equation

`y-y_1=m\left(x-x_1\right)`

substituting the values m = -1 and the point (4, 0)

`y-0 = -1 (x-4)`

Writing in the slope-intercept form

`y = -x+4`

Thus, the slope-intercept form of the equation of the line equation parallel to y=-x+ 2 will be:

• 
  `y = -x+4`

8)

Note: Your line is a little bit unclear. But, I am assuming the

ine is: y = -x-1

Given the assumed line

y = -x-1

We know that the slope-intercept form of the line equation is

`y=mx+b`

here

m is the slope and b is the intercept

Thus, the slope = m = -1

We know that a line perpendicular to another line contains a slope that is the negative reciprocal of the slope of the other line, such as:

slope = m = -1

perpendicular slope = – 1/m = -1/-1 = 1

Using point-slope of the line equation

`y-y_1=m\left(x-x_1\right)`

substituting the values m = 1 and the point (4, 3)

`y - 3 = 1 (x-4)`

Writing in the slope-intercept form

y-3 = x-4

y = x-4+3

y = x - 1

Thus, the slope-intercept form of the equation of the line equation perpendicular to y = -x-1 will be:

• y = x - 1