Question

PLEASE HELP AND ANSWER ALL QUESTIONS IF YOU CAN PLS AND TY.

Answer 1

(-1, 2.5) is yes, (11, 10) is yes, (70, 40) is no and (-2, 1.875) is yes.

Answer 2

(-1,2.5) is on the line.

(11,10) is on the line.

(70,40 is not on the line.

(-2, 1.875) is on the line.

Explanation:

First, find the equation of the line. Two write an equation in the slope -intercept form of the line we need a slope and the y-intercept. We can find this from the 2 points given (-5,0) and (3,5). The ordered pair is written in the from (x,y) The first number is how much we move right or left from the origin (0.0) and the second number tells us how much we move up or down from the origin (0,0).

To find the slope, we find the change in y over the change in x.

`((5-0))/(3 - -5))` =
`(5)/(3+ 5)` =
`(5)/(8)` Now we can use either of the points to find the y-intercept. Let's use (3,5)

slope =
`(5)/(8)`

x = 3

y =5

y=mx + b plug in what we know

5 =
`(5)/(8)`(3) + b This is the same as writing

5 =
`(5)/(8)`
`((3)/(1))` 3 and
`(3)/(1)` mean the same thing

5 =
`(15)/(8)` + b Now subtract
`(15)/(8)` from both sides of the equation

`(5)/(1)` -
`(15)/(8)` =
`(15)/(8)` -
`(15)/(8)` + b

`(40)/(8)` -
`(15)/(8)` = b

`(25)/(8)` = b Now we can write the equation

y = mx + b

y =
`(5)/(8)` x +
`(25)/(8)`

N ow that we have the equation, we can plug in the (x,y) and see if the equation is true or not. If the equation is true, the point is on the line.

(-1,2.5)

y =
`(5)/(8)` x +
`(25)/(8)`

2.5 =
`(5)/(8)`(-1) +
`(25)/(8)`

2.5 =
`(-5)/(8)` +
`(25)/(8)`

2.5 =
`(20)/(8)`

2.5 = 2.5

Yes, point (-1, 2.5) is on the line.

(11,10)

y = mx + b

10 =
`(5)/(8)`(11) +
`(25)/(8)`

10 =
`(55)/(8)` +
`(25)/(8)`

10 =
`(80)/(8)`

10 = 10

Yes, point (11,10) is on the line.

(70,40)

y = mx + b

40 =
`(5)/(8)`(70) +
`(25)/(8)`

40 =
`(350)/(8)` +
`(25)/(8)`

40 =
`(375)/(8)`

40 ≠ 46.875

Point (70,40) is not one the line.

(-2, 1.875)

y = mx + b

1.875 = (-2)
`(5)/(8)` +
`(25)/(8)`

1.875 =
`(-10)/(8)` +
`(25)/(8)`

1.875 =
`(15)/(8)`

1.875 = 1.875

Point (-2, 1.875) is on the line.