Question

Find the slope of the line simplify completely.

Answer 1

The slope of the line is
`\( (3)/(4) \)`, calculated by finding the change in ( y ) divided by the change in ( x ) and simplifying the fraction.

To find the slope of the line represented by the given data, we can use the formula for slope:
`\( \text{Slope} = \frac{\text{Change in } y}{\text{Change in } x} \)`. In this case, the values of ( x ) are -5, -1, and 3, corresponding to ( y ) values of 7, 10, and 13, respectively. The change in ( y ) is 13 - 7 = 6, and the change in ( x ) is ( 3 - (-5) = 8 ). Therefore, the slope is
`\( (6)/(8) \)`.

To simplify this fraction completely, we can divide both the numerator and denominator by their greatest common factor, which is 2. This results in a simplified slope of
`\( (3)/(4) \)`.

In summary, the slope of the line represented by the given data is
`\( (3)/(4) \)`, obtained by calculating the change in ( y ) divided by the change in ( x ), and simplifying the fraction by dividing both the numerator and denominator by 2.