Final answer:
The slope of the line represented by the equation 7y - 14x = -21 is 2, which is found by rearranging the equation into the slope-intercept form and identifying the coefficient of x.
Step-by-step explanation:
The question asks about the slope of the line represented by the equation 7y - 14x = -21. To find the slope, the equation needs to be arranged into slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
To convert the given equation to the slope-intercept form, first solve for y:
- Add 14x to both sides: 7y = 14x - 21.
- Divide every term by 7 to isolate y: y = 2x - 3.
Now that the equation is in the slope-intercept form, we can identify the slope m as 2. This tells us that for every increase of 1 on the horizontal axis, there is a rise of 2 on the vertical axis. The positive sign indicates that the line moves up as the x-value increases.