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,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Substituting the points (-3,2) and (3,2), we get;
[tex]m=\frac{2-4}{3+3}[/tex]
[tex]m=\frac{-1}{3}[/tex]
Thus, the slope of the line is [tex]m=\frac{-1}{3}[/tex]
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,
[tex]y=mx+b[/tex]
Substituting the values, we have;
[tex]y=-\frac{1}{3}x+3[/tex]
Thus, the equation of the line is [tex]y=-\frac{1}{3}x+3[/tex]
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
[tex]x=5-5=0[/tex]
Thus, x = 0 represents the year 2010.
To determine the y - value, let us substitute x = 0 in the equation [tex]y=-\frac{1}{3}x+3[/tex], we have;
[tex]y=-\frac{1}{3}(0)+3[/tex]
[tex]y=3[/tex]
Thus, for 2010 the value of y is 3.
