Write a linear function f with the values f(−1)=5 and f(3)=4.

1 Expert Answer When they say f(0) = -5 they mean the point (0, -5) is on the line. When they say f(3) = 4 they mean the point (3, 4) is on the line. In y = mx + b form, we would have f(x) = 3x - 5.

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boffeemadrid boffeemadrid · Answer 2 · 2021-11-05T17:04:07+01:00

The function is to be determined from the given points.

The linear function is [tex]f(x)=-\dfrac{1}{4}x+\dfrac{19}{4}[/tex]

The given values are

[tex]f(-1)=5[/tex]

[tex]f(3)=4[/tex]

The ordered pairs are [tex](-1,5),(3,4)[/tex]

The equation of the line is

[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)\\\Rightarrow y-5=\dfrac{4-5}{3-(-1)}(x-(-1))\\\Rightarrow y-5=-\dfrac{1}{4}(x+1)\\\Rightarrow y-5=-\dfrac{1}{4}x-\dfrac{1}{4}\\\Rightarrow y=-\dfrac{1}{4}x-\dfrac{1}{4}+5\\\Rightarrow y=-\dfrac{1}{4}x+\dfrac{19}{4}[/tex]

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