Find the value of a if the line joining the points (3a,4) and (a, -3) has a gradient of 1 ?

Question

Find the value of a if the line joining the points (3a,4) and (a, -3) has a gradient of 1 ?

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Khánh Gia 6 months 2021-07-31T13:12:17+00:00 2 Answers 84 views 0

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    0
    2021-07-31T13:13:33+00:00

    Answer:

     \frac{7}{2}

    Step-by-step explanation:

    Objective: Linear Equations and Advanced Thinking.

    If a line connects two points (3a,4) and (a,-3) has a gradient of 1. This means that the slope formula has to be equal to 1

    If we use the points to find the slope: we get

     \frac{4  +  3}{3a - a}

    Notice how the numerator is 7, this means the denominator has to be 7. This means the denomiator must be 7.

    3a - a = 7

    2a = 7

    a =  \frac{7}{2}

    0
    2021-07-31T13:13:39+00:00

    Answer:

    \displaystyle a=\frac{7}{2}\text{ or } 3.5

    Step-by-step explanation:

    We have the two points (3a, 4) and (a, -3).

    And we want to find the value of a such that the gradient of the line joining the two points is 1.

    Recall that the gradient or slope of a line is given by the formula:

    \displaystyle m=\frac{y_2-y_1}{x_2-x_1}

    Where (x₁, y₁) is one point and (x₂, y₂) is the other.

    Let (3a, 4) be (x₁, y₁) and (a, -3) be (x₂, y₂). Substitute:

    \displaystyle m=\frac{-3-4}{a-3a}

    Simplify:

    \displaystyle m=\frac{-7}{-2a}=\frac{7}{2a}

    We want to gradient to be one. Therefore, m = 1:

    \displaystyle 1=\frac{7}{2a}

    Solve for a. Rewrite:

    \displaystyle \frac{1}{1}=\frac{7}{2a}

    Cross-multiply:

    2a=7

    Therefore:

    \displaystyle a=\frac{7}{2}\text{ or } 3.5

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