Answer:
a, c, d
Step-by-step explanation:
because the slope intercep-t form of (0,5) and (2,8) is y = 1.5x + 5
you can check out the graph in desmos calculator, you just have to put y = 1.5x + 5
We want to find a line equation and with that, see which ones of the given points belong to that line.
The correct options are C: (6, 14) and D: (40, 60)
A general line equation is written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
If we know that the line passes through two points (x₁, y₁) and (x₂, y₂) then the slope can be written as:
[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Here we know that the line passes through (0,5) and (2, 8) then the slope is:
[tex]a = \frac{8-5}{2-0} = \frac{3}{2}[/tex]
We also can see that the line passes through (0, 5), meaning that the value of the y-intercept is b = 5.
So we can write our line as:
[tex]y = \frac{3}{2}*x + 5[/tex]
Now, let's see which points belong to this line.
To see this, we need to evaluate the line in the x-value of each one of these points and we need to see if the y-values coincide.
A) x = 5
[tex]y = \frac{3}{2}*5 + 5 = 12.5[/tex]
The values do not coincide with the ones of the point.
B) x = 5
We already see that for x = 5, y = 12.5, then this point does not belong to the line.
C) x = 6
[tex]y = \frac{3}{2}*6 + 5 = 14[/tex]
This point belongs to the line.
D) x = 30
[tex]y = \frac{3}{2}*30 + 5 = 50[/tex]
This point belongs to the line
E) x = 40
[tex]y = \frac{3}{2}*40 + 5 = 65[/tex]
This does not coincide with the y-value of the point, thus the point does not belong to the line.
Finally, we can conclude that the two correct options are C and D.
If you want to learn more, you can read:
https://brainly.com/question/2564656
