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  1. The constant of proportionality is [tex]\frac{9}{2}[/tex]

    Step-by-step explanation:

    The constant of proportionality is the ratio between two directly proportional quantities

    If x and y are in directly proportion, then [tex]\frac{y}{x}=k[/tex] , where k is the constant of proportionality.The direct proportion can be represented by a line whose equation is y = kx, where k is the slope of the line.

    To find the constant of proportionality from the given graph choose a point on the line and substitute x and y in the equation of the proportionality by the coordinates of the point.

    ∵ Point (4, 18) lies on the line

    ∴ x = 4, y = 18

    ∵ The equation is y = kx

    → Substitute x by 4 and y by 18

    ∴ 18 = k(4)

    ∴ 18 = 4k

    → Divide both sides by 4 to find k

    ∴ [tex]\frac{18}{4}=\frac{4k}{4}[/tex]

    ∴ [tex]\frac{18}{4}=k[/tex]

    → Simplify the fraction by dividing up and down by 2

    ∴ [tex]\frac{9}{2}=k[/tex]

    ∴ The constant of proportionality is [tex]\frac{9}{2}[/tex]

  2. Probably the sentence “They needed ways to move around in the city.

    Explanation: The paragraph would be fine without the sentence.

  3. The trend quickened after 1860 and continued throughout the 21st century as well.


    this one because you are telling the same thing basically with the whole article and the last sentence.

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