The expression of y in terms of x given that y = 2.5 and x = 1.5 is y = 2x - 0.5
In order to write y as a function of x, we will use the formula for calculating the equation of a line in the point-slope form expressed as:
y-y0 = m(x-x0) where:
m is the slope
(x0, y0) is any point on the given line,
From the graph, we know that:
[tex]\frac{\triangle y}{\triangle x} =\frac{4}{2}\\ \frac{\triangle y}{\triangle x} =2\\\frac{y-y_0}{x-x_0} = 2\\y-y_0=2(x-x_0)\\[/tex]
Given that x₀ = 1.5 and y₀ = 2.5
Substitute
[tex]y-2.5=2(x-1.5)\\y-2.5 = 2x - 3\\y = 2x-3+2.5\\y=2x-0.5\\[/tex]
This shows that the expression of y in terms of x is y = 2x - 0.5
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