Answer:
(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)
