A line contains the points (4,2) and (0, -1).What is the equation of the line?

Question

A line contains the points (4,2) and (0, -1).What is the equation of the line?

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Harper 1 month 2021-11-07T05:56:13+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-11-07T05:57:29+00:00

    Find the slope:

    y₂ – y₁ / x₂ – x₁

    -1 – 2 / 0 – 4

    -3 / -4

    3/4

    y = mx + b

    y = 3/4x + b

    Substitute any of the point’s coordinate in the equation.

    I’ll pick (0,-1)

    y = 3/4x + b

    -1 = 3/4(0) + b

    -1 = 0 + b

    -1 = b

    y-intercept = -1

    y-intercept Equation:

    y = 3/4x – 1

    Point-slope form:

    y – 2 = 3/4(x – 4)

    Standard form:

    -3/4x + y = -1

    0
    2021-11-07T05:58:08+00:00

    Answer: y = – 3x/4 + 5

    Step-by-step explanation:

    The equation of a straight line can be represented in the slope-intercept form, y = mx + c

    Where c = intercept

    Slope, m =change in value of y on the vertical axis / change in value of x on the horizontal axis represent

    change in the value of y = y2 – y1

    Change in value of x = x2 -x1

    y2 = final value of y

    y 1 = initial value of y

    x2 = final value of x

    x1 = initial value of x

    The line passes through (4,2) and (0, – 1),

    y2 = – 1

    y1 = 2

    x2 = 0

    x1 = 4

    Slope,m = (2 – – 1)/(0 – 4) = – 3/4

    To determine the y intercept, we would substitute x = 4, y = 2 and m= – 3/4 into

    y = mx + c. It becomes

    2 = – 3/4 × 4 + c

    2 = – 3 + c

    c = 2 + 3 = 5

    The equation becomes

    y = – 3x/4 + 5

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