Final answer:
The slope of the line given by the equation 22x - 5y = -8 is 22/5. This is found by rearranging the equation into slope-intercept form (y = mx + b), where the coefficient of x represents the slope.
Step-by-step explanation:
To find the slope of the line represented by the equation 22x - 5y = -8, we must first solve the equation for y to put it into the slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept.
Let's solve for y:
- 22x - 5y = -8
- -5y = -22x - 8 (Subtract 22x from both sides)
- y = (22/5)x + 8/5 (Divide both sides by -5 and simplify)
Now, the equation is in slope-intercept form, which is y = (22/5)x + 8/5. Here, the coefficient of x is (22/5), which is the slope of the line. Hence, the slope of the given line is 22/5.
Understanding the slope is crucial as it indicates the steepness and the direction of the line. For example, a positive slope indicates that the line ascends as the x-values increase, and the greater the absolute value of the slope, the steeper the line.