Mathematics
Grade10
Easy

Question

Ramona’s garage charges the following labor rates. All the customers are charged for at least 0.5 hr.

Write the linear function for the data in the table.

  1. f left parenthesis x right parenthesis equals 30 x plus 45
  2. f left parenthesis x right parenthesis equals 45 x plus 30
  3. f left parenthesis x right parenthesis equals 30 x minus 45
  4. f left parenthesis x right parenthesis equals 45 x minus 30

The correct answer is: f left parenthesis x right parenthesis equals 30 x plus 45


    The slope intercept form: y equals m x plus b
    The constant rate of change is 30. So, m = 30
    y equals 30 x plus b
    Substitute any ordered pair from the table.
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell 60 equals 30 cross times 0.5 plus b end cell row cell 45 equals b end cell end table
    So, the linear function is f left parenthesis x right parenthesis equals 30 x plus 45.

    A linear function forms a straight line in a graph. It is usually a polynomial function with a degree of 1 or 0, and the equation f(x) = mx + b, where b and m are real numbers. Isn't it similar to the slope-intercept form of a line, which is written as y = mx + b? Yes, because a linear function represents a line.
    ¶Examples from daily life
    1. To print logos on T-shirts, a t-shirt company charges a one-time charge of $50 and $7 per T-shirt. As a result, the total cost is given as a linear function f(x) = 7x + 50, where 'x' is the total number of t-shirts.
    2. In linear programming problems, linear functions represent an objective function to minimize costs or maximize profits.

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