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Sarah is keeping up with how many miles her car gets per gallon. She starts with a full tank. After 448 miles, she fills up with 14 gallons. If she plots the points (0,0) and (14,448) on a coordinate plane, what would be the y-value of the point (1,y)?

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1davey29
For starters, determine what the x and y coordinates mean. In this case, you have two numbers (not counting 0), 14 and 448. In the question, we can see that 14 is the number of gallons and 448 is the number of miles. As the point is (14,448) and points are set up as (x,y), we can determine that your x is your number of gallons and y is your number of miles. Now, we set up a ratio, which will be set up as [tex] \frac{miles_1}{gallons_1} = \frac{miles_2}{gallons_2} [/tex]. Using your known values as miles1 and gallons1 and your known x that is paired with the unknown y as miles2 and gallons2, we get [tex] \frac{448}{14} = \frac{y}{1} [/tex]. Now, as we have one in the denominator for our second ratio, we can simplify to [tex] \frac{448}{14} =y[/tex]. Now, we divide 448 by 14 to get 32, meaning our y value is 32 miles.

Using a linear function, it is found that the value is: y = 32.

A linear function has the following format:

[tex]y = mx + b[/tex]

In which:

  • m is the slope, which is the rate of change.
  • b is the y-intercept, which is the value of x when y = 0.

In this problem, when [tex]x = 0, y = 0[/tex], and thus, the y-intercept is [tex]b = 0[/tex].

Then

[tex]y = mx[/tex]

She also plots the point (14, 448), which means that when [tex]x = 14, y = 448[/tex], and this is used to find m.

[tex]14m = 448[/tex]

[tex]m = \frac{448}{14}[/tex]

[tex]m = 32[/tex]

Hence, the linear function is:

[tex]y = 32x[/tex]

Then, when x = 1, the point is (1,y), and:

[tex]y = 32(1) = 32[/tex]

The y-value is y = 32.

A similar problem is given at https://brainly.com/question/21567674

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