Question

HELP ME IM DESPERATE ITS DUE TMR

Answer 1

A) The gradient of
`L_(1)` is
`(-5)/(4)`

B) Point M is (2,2.5)

C) The gradient of
`L_(2)` is
`(4)/(5)`

y =
`(4)/(5)`x +
`(9)/(10)`

Explanation:

A)

The gradient is the slope. What is the
`(change in y)/(change in x)` (the change in y over the change in x)

From the two points given, if I start at point A and go to point B, I am going down 5 and then to the right 4, my y is decreasing by 5 while my x is increasing by 4, so the slope is:
`(-5)/(4)`

B)

We have two points (0,5) and (4,0) We want to find the middle of those two points. Ordered pairs are in the form (x,y) We will find the average of our x's and the average of our y's

x =
`(0+4)/(2)` = 2

y =
`(5+0)/(2)` 2.5

So the ordered pair in the middle is (2,2.5)

C)

Perpendicular lines have opposite inverse slopes. Since
`l_(1)`'s slope was
`(-5)/(4)`, the line that is perpendicular to it would be
`(4)/(5)`

To write the equation we will need the slope, and x(2) and a y(2,5) We are getting the (x,y) from point M (2,2.5)

y = mx + c

2.5 =
`(4)/(5)` (2) + c We are solving for C

2.5 =
`(8)/(5)` + c Subtract
`(8)/(5)` from both sides. I will convert 2.5 to
`(5)/(2)`

`(5)/(2)`-
`(8)/(5)` =
`(8)/(5)` -
`(8)/(5)` + c

`(25)/(10)` -
`(16)/(10)` = c

`(9)/(10)` = c

y =
`(4)/(5)`x +
`(9)/(10)`