Question

Given the table below, write a linear equation that defines the

dependent variable, a, in terms of the independent variable, p.

Someone help

Answer 1

a = 4p + 3

Explanation:

The general form of a linear equation is y = mx + b

where y is the dependent variable, x the independent variable

m = slope(rate of change)

b = y-intercept which is the value of y when x = 0

In this problem, instead of x we are asked to use p and instead of y we are using a

Therefore we get

a = mp + b

We have to compute m and b

Since b is the value of a when p = 0, we can easily see that a = 3 when p = 0

Therefore:
a = mp + 3

To determine m, take any value of p, find the corresponding a from the table, plug in these values and solve for m

When p = 1, a= 7

So we get

7 = m(1) + 3

7 = m + 3

or

m = 7-3 = 4

So the equation is
a = 4p + 3

You can verify this as correct by plugging in different values for p from the table and checking if you get the corresponding a value