The points (j, – 9) and ( – 10, – 4) fall on a line with a slope of – 1. What is the value of j?

Question

The points (j, – 9) and ( – 10, – 4) fall on a line with a slope of – 1. What is the value of j?

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Kiệt Gia 4 years 2021-09-02T08:19:26+00:00 1 Answers 8 views 0

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  1. Xavia
    0
    2021-09-02T08:20:50+00:00
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    Answer:

    The value of j = -5

    Step-by-step explanation:

    Given the points of the line

    • (j, – 9)
    • ( – 10, – 4)

    Slope m = -1

    To determine the value of j, we need to use the slope formula

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

    Here:

    • \left(x_1,\:y_1\right)=\left(j,\:-9\right)
    • \left(x_2,\:y_2\right)=\left(-10,\:-4\right )

    Now, substitute (x₁, y₁) = (j, -9)  and (x₂, y₂) = (-10, -4) in the formula

    m=\frac{-4-\left(-9\right)}{-10-j}

    We are already given m = -1. Therefore, we need to substitute m = -1 in the formula and solve for j

    -1=\frac{-4-\left(-9\right)}{-10-j}

    Multiply both sides by -10 –  j

    -1\cdot \left(-10-j\right)=\frac{5}{-10-j}\left(-10-j\right)

    Simplify

    -\left(-10-j\right)=5

    Divide both sides by -1

    \frac{-\left(-10-j\right)}{-1}=\frac{5}{-1}

    Simplify

    -10-j=-5

    Add 10 to both sides

    -10-j+10=-5+10

    Simplify

    -j=5

    Divide both sides by -1

    \frac{-j}{-1}=\frac{5}{-1}

    Simplify

    j=-5

    Therefore, the value of j = -5

    Verification:

    As the value of j = -5

    Now we have the points

    • (-5, – 9)
    • ( – 10, – 4)

    Now, we need to check whether the slope between the points (-5, -9) and (-10, -4) is -1 or not.

    Let us determine the slope between the points (-5, -9) and (-10, -4)

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

    Here:

    Now, substitute (x₁, y₁) = (-5, -9)  and (x₂, y₂) = (-10, -4) in the formula

    m=\frac{-4-\left(-9\right)}{-10-\left(-5\right)}

    m=\frac{-4+9}{-10+5}

    m=\frac{5}{-5}

    Apply fraction rule:  \frac{a}{-b}=-\frac{a}{b}

    m=-\frac{5}{5}

    m=-1

    Therefore, we verified that the slope of the line containing the points (-5, -9) and (-10, -4) is indeed m = -1.

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