Question

Which equation relates y to the x for the values in the table?

Answer 1

d) y= 7/2x minus 3/4

hope it helps

Answer 2

Answer:

D

Step-by-step explanation:

First, let's 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:

$y-y_1=m(x-x_1)$

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:

$y-\frac{11}{4}=\frac{7}{2}(x-1)$

Distribute:

$y-\frac{11}{4}=\frac{7}{2}x-\frac{7}{2}$

Add 11/4 to both sides. Note that 7/2 is the same as 14/4. So:

$y=\frac{7}{2}x-\frac{14}{4}+\frac{11}{4}$

Add:

$y=\frac{7}{2}x-\frac{3}{4}$

So, our answer is D.

And we're done!