Final answer:
The slope of the line represented by the equation 7x + 2y = 54 is -3.5. It is obtained by rearranging the equation into slope-intercept form and identifying the coefficient of x.
Step-by-step explanation:
To find the slope of the line represented by the equation 7x + 2y = 54, we should first express the equation in slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept.
To find the slope, we need to solve for y as follows:
- Rearrange the equation to isolate y on one side: 2y = -7x + 54.
- Divide both sides by 2 to solve for y: y = -7/2x + 27.
In the equation y = -7/2x + 27, the coefficient of x, which is -7/2, represents the slope. Therefore, the slope of the line is -3.5 (m = -7/2 = -3.5).