Final answer:
To find an additional linear relationship such that the solution of the system of lines is (30, 140), one can select any slope (m) and use the point to solve for the y-intercept (b) in the equation y = mx + b. For example, with slope 1, the y-intercept would be 110, leading to the equation y = x + 110.
Step-by-step explanation:
To determine which additional linear relationship could be added to the graph so that the solution of the system of the two lines would be (30, 140), we should follow these steps:
- Identify the point of intersection as the solution, which is given as (30, 140). This means when x=30, y should be 140.
- To create a linear relationship that intersects at this point, we can choose any slope (m) as long as the line passes through (30, 140).
- The general form of the equation of a line is y = mx + b, where m is the slope and b is the y-intercept. To determine the y-intercept (b), we can use the known point and choose a slope.
- If we choose a slope of 1 for simplicity, the equation becomes y = x + b. Substituting the point (30, 140) into the equation gives us 140 = 30 + b, which simplifies to b = 110.
- Therefore, a possible linear equation is y = x + 110.
It should be noted that many different lines can pass through the point (30, 140), so various slopes can be chosen to find different equations, as long as they satisfy the condition of passing through the given poin