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A linear function models the cost of renting a truck from a moving company. The table shows the cost y (in dollars) when you drive the truck z miles
Graph the function. Compare the slope and the y-intercept of the graph with the slope and the c-intercept of the graph of c() 0.52 + 70
Miles, x
Cost
(dollars), y
40
0
50
80
100
120

Respuesta :

MrRoyal

The equation and the table are illustrations of linear functions.

  • The equation has a greater y-intercept
  • The table has a greater slope

The function is given as:

[tex]\mathbf{c(x) = 0.5x + 70}[/tex]

The table is given as:

[tex]\mathbf{\left[\begin{array}{cccccc}x&0&1&4&6&8\\y&40&50&80&100&120\end{array}\right] }[/tex]

The slope and y-intercept of the equation

To calculate the y-intercept, we simply set x to 0.

So, we have:

[tex]\mathbf{c(x) = 0.5x + 70}[/tex]

[tex]\mathbf{c(0) = 0.5 \times 0 + 70}[/tex]

[tex]\mathbf{c(0) = 0 + 70}[/tex]

[tex]\mathbf{c(0) = 70}[/tex]

This means that:

[tex]\mathbf{y-intercept = 70}[/tex]

The coefficient of x, represents the slope.

So, we have:

[tex]\mathbf{Slope = 0.5}[/tex]

The slope and y-intercept of the equation

To calculate the y-intercept, we simply take the value of y, when x= 0.

From the table,

y = 40, when x = 0

So:

[tex]\mathbf{y-intercept = 40}[/tex]

The slope of the function, is calculated using:

[tex]\mathbf{Slope = \frac{y_2 - y_1}{x_2 - x_1}}[/tex]

From the table:

[tex]\mathbf{(x_1,y_1) = (0,40)}[/tex]

[tex]\mathbf{(x_2,y_2) = (1,50)}[/tex]

So, we have:

[tex]\mathbf{Slope = \frac{50 - 40}{1 - 0}}[/tex]

[tex]\mathbf{Slope = \frac{10}{1}}[/tex]

[tex]\mathbf{Slope = 10}[/tex]

By comparing the slopes and the y-intercepts, the conclusions are:

  • The equation has a greater y-intercept
  • The table has a greater slope

Read more about slopes and y-intercepts at:

https://brainly.com/question/12763756

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