Question

5 Which equation represents the relationship between the x-values and the y. the table? у 2 16 4 28 6 40 10 64 Ay= 2x + 12 By= 4x + 6 C y = 2x + 4 Dy = 6x + 4 Page 5 1 8 a +

Answer 1

The linear equation is;

`y\text{ =6x + 4}`

Here, we want to get the linear equation between the variables on the table

The general form is;

`y\text{ = mx + b}`

where m is the slope and b is the y-intercept

The y-intercept is the the value of y when x is 0

As we can see from the table, the value of y-intercept is 4

So, we have the partially complete equation as;

`y\text{ = mx + 4}`

To get the value of m, we can substitute any point

Let us use the point (4,28)

We simply substitute 4 for x and 28 for y

Thus, we have;

`\begin{gathered} 28\text{ = 4(m) + 4} \\ 4m\text{ = 28-4} \\ 4m\text{ = 24} \\ m\text{ = }(24)/(4)\text{ = 6} \end{gathered}`

The equation is thus;

`y\text{ = 6x + 4}`