Answer:
We conclude that the function [tex]f(x) = 12x + 28[/tex] works.
The graph of the function y = 12x + 28 is also attached below.
Step-by-step explanation:
Given that the line passes through the points
Let us determine the slope between (-1, 16) and (5, 88) using the slope formula
[tex]\mathrm{m}=\frac{y_2-y_1}{x_2-x_1}[/tex]
where m is the slope between (x₁, y₁) and (x₂, y₂)
In our case:
so subtituting (x₁, y₁) = (-1, 16) and (x₂, y₂) = (5, 88) in the slope formula
[tex]\mathrm{m}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{88-16}{5-\left(-1\right)}[/tex]
Refine
[tex]m=12[/tex]
Thus, the slope of the line is: m = 12
Important Tip:
The slope-intercept form of the line equation is
[tex]y = mx + b[/tex]
where m is the slope and b is the y-intercept
now substituting m = 12 and the point (-1, 16) in the slope-intercept form of the line equation
[tex]y = mx + b[/tex]
[tex]16 = 12(-1) + b[/tex]
switch the equation
[tex]12(-1) + b = 16[/tex]
[tex]-12 + b = 16[/tex]
Add 12 to both sides
[tex]-12+b+12=16+12[/tex]
Simplify
[tex]b=28[/tex]
Thus, the y-intercept of the line is: b = 28
now substituting m = 12 and b = 28 in the slope-intercept form of the line equation
[tex]y = mx + b[/tex]
[tex]y = 12x + 28[/tex]
Thus the equation of the line is:
[tex]y = 12x + 28[/tex]
or
[tex]f(x) = 12x + 28[/tex] ∵ [tex]y = f(x)[/tex]
Hence, we conclude that the function [tex]f(x) = 12x + 28[/tex] works.
The graph of the function y = 12x + 28 is also attached below.
