To determine the equations of the lines described, we need to identify the properties of each line based on their slopes and intercepts.
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Solid Line: It's mentioned that the equation of the solid line is \( y = mx \), which means it is a linear equation that passes through the origin (0, 0). To identify the slope (m), look for two points on this line. For example, if the line passes through (1, 1), the slope would be 1; thus the equation would be \( y = x \).
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Dotted Line: The equation of the dotted line is in the form \( y = mx + b \). You need to find the slope and y-intercept of this line. If you look for points where this line intersects the grid, such as where it crosses the y-axis (the y-intercept, b) and find its slope (by identifying another point it passes through), you can derive the equation.
Let's suppose you find that the dotted line has a slope of 1 and a y-intercept of 2. In that case, the equation would be \( y = x + 2 \).
Combining these results gives:
- The equation of the solid line: \( y = x \)
- The equation of the dotted line: \( y = x + 2 \)
If you have specific coordinates of the points where the lines intersect the axes, you can replace these values accordingly.
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