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Answer:
We conclude that the equation of a linear function with f (5) = -1 and f(0) = -5 will be:
Step-by-step explanation:
Given
f(5) = -1 means at x = 5, y = -1
Hence, the point (5, -1) lies on the line function.
f(0) = -5 means at x = 0, y = -5
Hence, the point (0, -5) lies on the line function.
Thus, the two points on the linear line function graph are:
Finding the slope between the points (5, -1) and (0, -5)
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(5,\:-1\right),\:\left(x_2,\:y_2\right)=\left(0,\:-5\right)[/tex]
[tex]m=\frac{-5-\left(-1\right)}{0-5}[/tex]
[tex]m=\frac{4}{5}[/tex]
The slope-intercept form of the linear line function
[tex]y = mx+b[/tex]
where m is the slope and b is the y-intercept
We have already determined the slope which is: m = 4/5
We know the y-intercept can be determined by setting x = 0 and solving for y.
Thus, the point (0, -5) represents the y-intercept b = -5.
Now, substituting m = 4/5 and b = -5 in the slope-intercept form
[tex]y = mx+b[/tex]
y = 4/5x + (-5)
y = 4/5x - 5
Therefore, we conclude that the equation of a linear function with f (5) = -1 and f(0) = -5 will be: