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Answer:
[tex]y = -5x -2[/tex]
Step-by-step explanation:
Given:
[tex]g(x) = x^2 -2x[/tex]
Solving for [tex]\bold{g(-4)}[/tex]:
[tex]g(-4) = (-4)^2 -2(-4) \\ g(-4) = 16 +8 \\ g(-4) = 24[/tex]
This means that [tex](-4,g(-4))[/tex] is an equivalent statement of [tex](-4,24)[/tex].
Solving for [tex]\bold{g(1)}[/tex]:
[tex]g(1) = (1)^2 -2(1) \\ g(-4) = 1 -2 \\ g(-4) = -1[/tex]
This means that [tex](1,g(1))[/tex] is an equivalent statement of [tex](1,-1)[/tex].
Now we have the two points of the line, [tex](-4,24)[/tex] and [tex](1,-1)[/tex], we can finally solve for its slope, [tex]m[/tex]. Recall that [tex]m = \frac{y_2 -y_1}{x_2 -x_1}\\[/tex].
[tex]m = \frac{-1 -24}{1 -(-4)} \\ m = \frac{-25}{5} \\ m = -5[/tex]
Now that we know our slope, we can then write it as point-slope form and then rewrite it in its slope-intercept form as we are asked. Recall that an equation of a line in its point-slope form is write, [tex]y -y_1 = m(x -x_1)[/tex], where [tex]y_1[/tex] and [tex]x_1[/tex] is [tex]y[/tex] and [tex]x[/tex] coordinates of any point of a line respectively.
Writing for the equation of a line in its point-slope form with the point [tex]\bold{(1,-1)}[/tex]:
[tex]y -(-1) = -5(x -1) \\ y +1 = -5(x -1)[/tex]
Rewriting for the equation of a line in its slope-intercept form:
[tex]y +1 = -5(x -1) \\ y +1 = -5x -1 \\ y = -5x -2[/tex]