Question

If the units for x are years, and x = 5 represents the year 2015, what is the y-value for 2010?

Answer 1

Given:

The given graph passes through the points (-3,4) and (3,2)

The x - axis represents the years. The value x = 5, year 2015.

We need to determine the y - value for 2010.

Slope:

The slope of the line can be determined using the formula,

`m=(y_2-y_1)/(x_2-x_1)`

Substituting the points (-3,2) and (3,2), we get;

`m=(2-4)/(3+3)`

`m=(-1)/(3)`

Thus, the slope of the line is
`m=(-1)/(3)`

y - intercept:

The y - intercept in the graph is the point in the line that crosses the y - axis.

Thus, from the graph, it is obvious that the y - intercept is b = 3.

Equation of the line:

The equation of the line can be determined using the formula,

`y=mx+b`

Substituting the values, we have;

`y=-(1)/(3)x+3`

Thus, the equation of the line is
`y=-(1)/(3)x+3`

The y - value for 2010:

Since, it is given that x = 5 represents 2015 and 2010 is 5 years before 2010.

Hence, the value of x for 2010 is given by

`x=5-5=0`

Thus, x = 0 represents the year 2010.

To determine the y - value, let us substitute x = 0 in the equation
`y=-(1)/(3)x+3`, we have;

`y=-(1)/(3)(0)+3`

`y=3`

Thus, for 2010 the value of y is 3.