Final answer:
To solve the equation 49x + 7y = 21, subtract 49x from both sides, then divide by 7, resulting in the equation y = 3 - 7x which represents a straight line with a slope of -7 and a y-intercept of 3.
Step-by-step explanation:
To solve the equation 49x + 7y = 21 for y, we will rearrange the equation to isolate y on one side. The aim is to express y in terms of x, making it easy to understand the relationship between these two variables. Here's how you can solve it:
- First, subtract 49x from both sides of the equation to get 7y = 21 - 49x.
- Then, divide both sides by 7 to isolate y, giving us y = (21 - 49x) / 7.
- Simplify the equation to get y = 3 - 7x.
This final equation y = 3 - 7x represents a straight line with a slope of -7 and a y-intercept of 3. The slope of the line indicates how steep the line is, and the y-intercept is the point where the line crosses the y-axis. Thus, this linear equation showcases the inverse relationship between x and y; as x increases, y decreases.
The result y = 3 - 7x can further be verified by plotting it on a graph or by constructing a table where different values of x will result in corresponding values of y, which align with the equation of the line.