Suppose the constant rate of change of y with respect to x is 8.5, and the value of y is 5 when the value of x is 11. what is the value of y when the value of x is 19? what is the value of y when the value of x is –1? what is the value of x when the value of y is 7?

Step-by-step explanation:

You are given a point and a slope, so you can write the linear equation relating x and y using the point-slope form of the equation for a line. That form for slope m and point (h, k) is ...

  y = m(x -h) +k

For your given values, m = 8.5, and (h, k) = (11, 5), the equation relating x and y can be written ...

  y = 8.5(x -11) +5

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Evaluating this for several different x-values can be done with a spreadsheet or calculator. I like to write the function into a graphing calculator and let it do the tedious arithmetic. (See the attachment.)

However, to show you what is involved in doing this by hand, we can ...

  let x = 19, then ...

  y = 8.5(19 -11) +5 = 8.5·8 +5 = 73

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  let x = -1, then ...

  y = 8.5(-1-11) +5 = 8.5·(-12) +5 = -97

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To find the value of x for y=7, we can realize that to make y go up by 2 (from the given point of 5), we need to have x go up by 2/8.5 (from the given point of 11). That is ...

  for y = 7 ...

  x = 11 + 2/8.5 = 11 + 4/17 = 11 4/17