Question

Write an equation to represent the relationship between the independent and dependent quantities in the following table.

Answer 1

y = x + 4

Explanation:

We want to form an equation to represent the table. I will form an equation in standard y-intercept form. I can either calculate the slope mathematically, or look at the table and see that as x increases by 1, so does the respective value of y.

y = mx + b

m is slope and b is the y-intecept.

`m = (-2 - (-3))/(2-1) \\m = (-2 + 3)/(2 - 1)\\m = (1)/(1) \\m = 1`

So now we have the slope of our equation.

y = x + b

We can find the y-intecept two ways, use the table, or plug in a point from the table in calculate b from our equation. Should we choose to use the table, remember that y-intercept means that at that point x = 0. Following the pattern from the table, we can infer that when x = 0, y = -4. So the y-intercept of the function is -4.

y = x + b

Substitute the point (4, 0) into the equation to calculate b.

0 = 4 + b

b = -4

So our equation of the function is y = x + 4.

You can check this by substituting any point from the table into our equation.