Answer:
D
Step-by-step explanation:
First, we can determine what type of relationship we are dealing with by examining the table.
From x = 1 to x = 2, the y-value increased by 14/4 (25/4-11/4).
From x = 2 to x = 3, the y-value also increased by 14/4 (39/4-25/4)
And from x = 3 to x = 4, the y-value still increased by 14/4 (53/4-39/4).
Therefore, we can conclude that our table represents a linear relationship.
And since it increases by 14/4 or 7/2 for every x, this means that our slope is 7/2.
The only choice that represents a linear equation with a slope of 7/2 is D. So, the correct answer is D.
However, we can confirm our answer by writing our equation. We can use the point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
Where m is the slope and (x₁, y₁) is a point.
Let's substitute 7/2 for m. We can pick any point, so I'm going to use (1, 11/4) for (x₁, y₁).
Substitute:
[tex]\displaystyle y-\frac{11}{4}=\frac{7}{2}(x-1)[/tex]
Distribute:
[tex]\displaystyle y-\frac{11}{4}=\frac{7}{2}x-\frac{7}{2}[/tex]
Add 11/4 to both sides. Note that 7/2 is the same as 14/4. So:
[tex]\displaystyle y=\frac{7}{2}x-\frac{14}{4}+\frac{11}{4}[/tex]
Add:
[tex]\displaystyle y=\frac{7}{2}x-\frac{3}{4}[/tex]
So, our answer is D.
And we're done!
