What is the slope of the line that passes through the points (5, 1) and (2, -7)?

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What is the slope of the line that passes through the points (5, 1) and (2, -7)?

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Orla Orla 1 month 2021-08-13T20:10:07+00:00 2 Answers 0 views 0

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    0
    2021-08-13T20:11:12+00:00

    Answer:

    m [ slope ] = 8/3

    Step-by-step explanation:

    What is the slope of the line that passes through the points (5, 1) and (2, -7)?

    m = ∆y / ∆x

    m = y₂ – y₁ / x₂ – x₁

    | (5, 1) → (x₁, y₁) | (2, -7) → (x₂, y₂) |

    [each coordinate will correspond (directly go to) to the variables shown]

    m = (-7) – (1) / (2) – (5)

    m = -8 / -3

    m = 8 / 3

    This means that this line has a rise of 8 and a run of 3.

    Up 8 and right 3 proportionally, it would touch the opposite corners of a plane that was 8 by 3 units.

    Slope can be thought of as the steepness of a line, the greater the slope, the greater the steepness.

    These points are generally known as cartesian coordinates.

    ____________

    Once you have the slope, you can back track from one of the coordinates to find the equation of the line.

    Just multiply the slope by the x of either coordinate, make it opposite, and then add that to the y of that coordinate to get b [the y-intercept; where it crosses the y axis, x is always 0]

    Since (2, -7) is closer to the y axis than (5, 1) it is more convenient.

    In (2, -7), 2 is the x variable and -7 is the y variable.

    -mx + y = (-8/3)(2) + (-7) = -16/3 + (-21/3)

    21/3 is the same as 7 [so it will have a common denominator].

    -16 + -21 / 3 = -37/3 = b

    Thus this line has an equation of

    y = mx + b

    ↓ ↓

    y = 8/3x – 37/3.

    __________________________

    Or you can refer to point slope which is what is taught:

    y – y₁ = m(x – x₁).

    You can tell that there are some similarities to this and the slope formula.

    m = ( y₂ – y₁ / x₂ – x₁ ) →

    m × ( x₂ – x₁ ) =

    ( y₂ – y₁ / x₂ – x₁ ) × ( x₂ – x₁ )

    [multiply the denominator by both sides]

    m ( x₂ – x₁ ) = y₂ – y₁

    [x₂, and y₂ can just be x and y since you only need the initial coordinate and slope, because the second coordinate can be anything along that line]

    m ( x – x₁ ) = y – y₁ →

    y – y₁ = m(x – x₁)

    [symmetric property of equality]

    if a = b, b = a.

    0
    2021-08-13T20:11:26+00:00

    -7-1/2-5 because to solve, you do y2-y1/x2-x1
    So you get -6/-3, which equals 2
    SLOPE IS 2

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