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31 December, 08:56

Write an equation in slope intercept form for $750 and $600 and $1150

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  1. 31 December, 09:22
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    y = 0.5x + 10

    Step-by-step explanation:

    Step 1:

    Identify the independent and dependent variables.

    The independent variable (x) is the square footage of floor space.

    The dependent variable (y) is the monthly rent.

    Step 2:

    Write the information given in the problem as ordered pairs.

    The rent for 600 square feet of floor space is $750:

    (600, 750)

    The rent for 900 square feet of floor space is $1150:

    (900, 1150)

    Step 3:

    Find the slope.

    m = (y₂ - y₁) / (x₂ - x₁)

    Substitute (600, 750) for (x₁, y₁) and (900, 1150) for (x₂, y₂).

    m = (1150 - 750) / (900 - 600)

    m = 400 / 300

    m = 4/3

    Step 4:

    Find the y-intercept.

    Use the slope 4/3 and one of the ordered pairs (600, 750).

    Slope-intercept form:

    y = mx + b

    Plug m = 4/3, x = 600 and y = 750.

    750 = (4/3) (600) + b

    750 = (4) (200) + b

    750 = 800 + b

    -50 = b

    Step 5:

    Substitute the slope and y-intercept.

    Slope-intercept form

    y = mx + b

    Plug m = 4/3 and b = - 50

    y = (4/3) x + (-50)

    y = (4/3) x - 50

    Problem 2:

    Hari's weekly allowance varies depending on the number of chores he does. He received $16 in allowance the week he did 12 chores, and $14 in allowance the week he did 8 chores. Write an equation for his allowance in slope-intercept form.

    Solution:

    Step 1:

    Identify the independent and dependent variables.

    The independent variable (x) is number of chores Hari does per week

    The dependent variable (y) is the allowance he receives per week.

    Step 2:

    Write the information given in the problem as ordered pairs.

    For 12 chores, he receives $16 allowance:

    (12, 16)

    For 8 chores, he receives $14 allowance:

    (8, 14)

    Step 3:

    Find the slope.

    m = (y₂ - y₁) / (x₂ - x₁)

    Substitute (12, 16) for (x₁, y₁) and (8, 14) for (x₂, y₂).

    m = (14 - 16) / (8 - 12)

    m = (-2) / (-4)

    m = 1/2

    m = 0.5

    Step 4:

    Find the y-intercept.

    Use the slope 0.5 and one of the ordered pairs (8, 14).

    Slope-intercept form:

    y = mx + b

    Plug m = 0.5, x = 8 and y = 14.

    14 = (0.5) (8) + b

    14 = 4 + b

    10 = b

    Step 5:

    Substitute the slope and y-intercept.

    Slope-intercept form

    y = mx + b

    Plug m = 0.5 and b = 10

    y = 0.5x + 10
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