Question

Lots of points and not really hard and wont take too long to solve!!! plz help​

Answer 1

see explanation

Explanation:

19

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c yje y- intercept )

y = 2x - 3 is in this form with slope m = 2

• Parallel lines have equal slopes, hence

y = 2x + c ← partial equation of parallel line

To find c substitute (- 1, 2) into the partial equation

2 = - 2 + c ⇒ c = 2 + 2 = 4

y = 2x + 4 ← equation of parallel line

20

Rearrange x - 3y = 5 into slope- intercept form

Subtract x from both sides

- 3y = - x + 5 ( divide all terms by - 3 )

y =
`(1)/(3)` x -
`(5)/(3)` ← in slope- intercept form

with slope m =
`(1)/(3)`

Given a line with slope m then the slope of a line perpendicular to it is

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/((1)/(3) )` = - 3, so

y = - 3x + c

The line passes through (0, 6) ⇒ c = 6

y = - 3x + 6 ← equation of perpendicular line

Answer 2

Here all you need to know to solve this exercise:

1) When you write the equation of a line in the form

`y=mx+q`

the slope is the coefficient m.

2) When you know that the line passes through a point
`(x_0,y_0)` and has slope m, the equation of the line is given by

`y-y_0=m(x-x_0)`

3) Let
`m_1,m_2` be the slopes of two lines. If the lines are parallel, then
`m_1=m_2`. If the lines are perpendicular, then
`m_1m_2=-1`.

In the first exercise, using point 1, you can see that the slope of the given line is 2. We want a parallel line passing through the given point. So, our line has the same slope, and its equation is (see point 2)

`y-2=2(x+1) \iff y = 2x+4`

Similarly, in the second exercise, the original slope is 1/3, so the perpendicular slope is -3. The equation will be, imposing the passage through the given point,

`y-6 = -3(x-0) \iff y = -3x+6`