For the equation y = 2.5X, choose which ordered pairs would be on the line if it was graphed? Select ALL that apply. (0, 0) and (-4, -10)

(-1, -2.5)

(0. 0) and (2, 5)

(3, 7.5) and (-3, -7.5)

(1, 3.5) and (2, 5)

(1, 2.5) and (3, 6.5)

(0, 0) and (-4, -10)

(0. 0) and (2, 5)

(3, 7.5) and (-3, -7.5)

Step-by-step explanation:

We have the function:

y = 2.5*x

This is a linear relationship, with a slope equal to 2.5 and y-intercept equal to zero.

A linear relationship can be written as:

y = a*x + b

where a is the slope and b is the y-axis intercept.

For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:

a = (y2 - y1)/(x2 - x1).

Then we can check with the points given in the options, and see which ones meet these two criteria.

a) (0, 0) and (-4, -10)

the slope will be:

a = (-10 - 0)/(-4 - 0) = 2.5

The slope is 2.5, then:

y = 2.5*x + b

To find the value of b, we just need to replace the values of one of the points in the equation, let's use the point (0, 0)

0 = 2.5*0 + b

0 = 0 + b

Then b = 0

y = 2.5*x

This means that these points would be on the line when graphed.

b) (0. 0) and (2, 5)

in this case the slope is:

a = (5 - 0)/(2 - 0) = 2.5

then:

y = 2.5*x + b

to find the value of b, let's use the point (0, 0)

0 = 2.5*0 + b

0 = 0 + b

b = 0

then

y = 2.5*x

This ordered pair would be on the line when graphed.

c) (3, 7.5) and (-3, -7.5)

The slope is:

a = (-7.5 - 7.5)/(-3 - 3) = 2.5

y = 2.5*x + b

The value of b will be obtained by using the point (3, 7.5)

7.5 = 2.5*3 + b

7.5 = 7.5 + b

b = 0

Then:

y = 2.5*x

This ordered pair will be on the line when graphed.

d) (1, 3.5) and (2, 5)

The slope is:

a = (5 - 3.5)/(2 - 1) = 1.5

The slope is different than 2.5, then we can discard this pair.

e) (1, 2.5) and (3, 6.5)

the slope is:

a = (6.5 - 2.5)/(3 - 1) = 2

Again, the slope is different than 2.5, then this option can be discarded.

We can conclude that the ordered pairs that will be graphed are:

(0, 0) and (-4, -10)

(0. 0) and (2, 5)

(3, 7.5) and (-3, -7.5)