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,

$m=\frac{y_2-y_1}{x_2-x_1}$

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

$m=\frac{2-4}{3+3}$

$m=\frac{-1}{3}$

Thus, the slope of the line is $m=\frac{-1}{3}$

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;

$y=-\frac{1}{3}x+3$

Thus, the equation of the line is $y=-\frac{1}{3}x+3$

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 $y=-\frac{1}{3}x+3$, we have;

$y=-\frac{1}{3}(0)+3$

$y=3$

Thus, for 2010 the value of y is 3.