Final answer:
The slope of the line defined by the equation 5y - 7x + 3 = 0 is 7/5. This is found by rearranging the equation to the slope-intercept form y = mx + b and identifying the coefficient of x as the slope.
Step-by-step explanation:
The question asks to determine the slope of the line defined by the equation 5y - 7x + 3 = 0. The slope of a line in its standard form Ax + By = C can be found by solving the equation for y to get it into slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept. To solve for y, we rearrange the equation as follows:
- Add 7x to both sides to get 5y = 7x + 3.
- Divide all terms by 5 to isolate y, yielding y = (7/5)x + 3/5.
The coefficient of x in this equation is 7/5, which is the slope of the line. Therefore, the slope of the line 5y - 7x + 3 = 0 is 7/5.
Understanding the concept of the slope is fundamental in the Algebra of Straight Lines. The slope determines how steep a line is and whether it rises or falls as you move from left to right across the graph. A positive slope, like the one we found, indicates a line that rises as we move to the right.