Question

find the slope of the line that passes through the given coordinates

1. \\((-1, 6)\\) and \\((4, 3)\\)
2. \\((29, 11)\\) and \\((-3, -7)\\)
3. \\((11, 7)\\) and crosses the y-axis at 17.

use your knowledge of slope and rate of change to answer the following questions.

1. a linear function \\(f(x)\\) contains the coordinates \\((-9, 4)\\) and \\((6, 4)\\). joy says \\(f(x)\\) is a horizontal line, and lu says \\(f(x)\\) is a vertical line. which student correctly described the function? explain.
2. ... filled his gas tank with 16 gallons of ... the table shows the linear relationship ... the amount of gas remaining in his ... the miles driven. what is the rate of ... of gas per mile driven?
3. find the slope of the graphed line

Explanation:

Calculate the slope of the function

$$ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{4 - 4}{6 - (-9)} = \frac{0}{15} = 0 $$

Determine the orientation of the line

$$ y = 4 \implies \text{horizontal line} $$

Identify the correct student

$$ \text{Joy is correct.} $$

Answer:

Joy correctly described the function. Since both coordinates have the same \(y\)-value of \(4\), the line is horizontal with a slope of \(0\).