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Use the image to answer the question././././././.

A line graph with x-axis ranging from 0 to 6 in unit increment and y-axis ranging from 0 to 60 in increments of 10.

Luis rents a paddleboat to use at West Park for the day. He has to pay a deposit and an hourly fee. Using information from the graph, enter the values that complete the equation for this situation. plotted points 2, 30 and 4,40

(1 point)
y=
x+

1 answer

To determine the equation of the line represented by the plotted points (2, 30) and (4, 40), we need to establish the slope (m) and the y-intercept (b) of the linear equation in the form of \( y = mx + b \).

  1. Calculate the slope (m): \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{40 - 30}{4 - 2} = \frac{10}{2} = 5 \]

  2. Use the slope and a point to find the y-intercept (b): Using point (2, 30): \[ 30 = 5(2) + b \] \[ 30 = 10 + b \] \[ b = 30 - 10 = 20 \]

  3. Form the final equation: \[ y = 5x + 20 \]

Now, completing the equation based on the structure you provided:

\( y = 5x + 20 \)

So, the values to enter are: y = 5x + 20.