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Mathematics

1 answer:

Ivanshal [37]3 years ago

8 0

Answer:

1) the constant variation is B) -2

3) the equation of the line is C) y=2/3x+9

4) the equation of the line is D) y=2x-5

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$\large\boxed{f(x)=\dfrac{3}{2}x-1}$

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$\text{The slope-intercept formula:}\\\\y=mx+b\\\\m\ -\ slope\\b\ -\ y-intercept\\\\\text{The formula of a slope:}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\\\\text{From the table we hve two points (0, -1) and (2, 2). Substitute:}\\\\m=\dfrac{2-(-1)}{2-0}=\dfrac{3}{2}$

$\text{Therefore the equation is}\ f(x)=\dfrac{3}{2}x-1\\\\\text{Check for the point (4, 5):}\\\\f(4)=\dfrac{3}{2}(4)-1=(3)(2)-1=6-1=5\qquad\ CORRECT$