Answer:
[tex]y = \frac{1}{4}x +\frac{7}{4}[/tex]
Step-by-step explanation:
Given
[tex]f(-3) = 1[/tex]
[tex]f(13) = 5[/tex]
Required
Determine the linear function
A function is of the form:
[tex]y = f(x)[/tex]
Writing the given parameters in (x,y) format, we have:
[tex]f(-3) = 1[/tex] implies (-3,1)
[tex]f(13) = 5[/tex] implies (13,5)
So, the x and y values are:
(-3,1) and (13,5)
i.e.
[tex](x_1,y_1) = (-3,1)[/tex]
[tex](x_2,y_2) = (13,5)[/tex]
First, we need to determine the slope using:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{5 - 1}{13 - -(3)}[/tex]
[tex]m = \frac{4}{13 +3}[/tex]
[tex]m = \frac{4}{16}[/tex]
[tex]m = \frac{1}{4}[/tex]
The equation is calculated as thus:
[tex]y - y_1 = m(x - x_1)[/tex]
Where
[tex](x_1,y_1) = (-3,1)[/tex]
[tex]m = \frac{1}{4}[/tex]
[tex]y - 1 = \frac{1}{4}(x - (-3))[/tex]
[tex]y - 1 = \frac{1}{4}(x +3)[/tex]
[tex]y = \frac{1}{4}(x +3) + 1[/tex]
[tex]y = \frac{1}{4}x +\frac{3}{4} + 1[/tex]
[tex]y = \frac{1}{4}x +\frac{3+4}{4}[/tex]
[tex]y = \frac{1}{4}x +\frac{7}{4}[/tex]
