If a line passes through the points (-5,-4) and (3,-1), the equation of the line is?

Question

If a line passes through the points (-5,-4) and (3,-1), the equation of the line is?

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    0
    2021-10-13T22:29:48+00:00

    y = \frac{3}{8} x – \frac{17}{8}

    the equation of a line in slope- intercept form is

    y = mx + c ( m is the slope and c the y-intercept )

    to calculate m use the gradient formula

    m = (y₂ – y₁ ) / (x₂ – x₁ )

    with (x₁, y₁ ) = (- 5, – 4 ) and (x₂, y₂ ) = (3 , – 1 )

    m = \frac{-1+4}{3+5} = \frac{3}{8}

    the partial equation is y = \frac{3}{8} x + c

    to find c substitute either of the 2 points into the partial equation

    using (3, – 1 ), then

    – 1 = \frac{9}{8} + c ⇒ c = – \frac{17}{8}

    y = \frac{3}{8} x – \frac{17}{8} ← in slope-intercept form

    0
    2021-10-13T22:30:05+00:00

    answer: y = 1.5x – 5.5

    explanation:

    use y = mx +b to model your equation

    (m = slope, b = y-intercept)

    let’s start by finding slope

    to find slope, subtract the y values over the x values.

    – 4 – (-1) / – 5 – (-3)

    solve and simplify.

     -3 / -2

    two negatives equals a positive, so convert into a decimal and remove the negative

    you get 1.5.

    now, plug the slope a y and x value into the equation to find b, the missing value.

    -1 = 1.5(3) + b

    -1 = 4.5 + b

    -5.5= b

    so, your equation is y = 1.5x – 5.5.

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