To determine the equations of the solid line and the dotted line based on the intersection seen on the coordinate plane, we need to analyze their slopes and y-intercepts.
Assuming the solid line has a slope of 1, we can express its equation in slope-intercept form, which is:
\[ y = mx + b \]
where \( m \) is the slope and \( b \) is the y-intercept.
For the solid line (assuming slope \( m = 1 \)), the equation would look like:
\[ y = 1x + b \]
Next, for the dotted line, it is given that it has a different slope and possibly a y-intercept shift.
To find the specific equations:
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If the solid line passes through the origin, its equation is: \[ y = x \]
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For the dotted line, we would need the slope (let's assume it’s different from 1) and its y-intercept (let's assume it's some constant \( c \)). The equation would look something like: \[ y = mx + c \]
If we could visually confirm from the graph, we'd know its slope (\( m \)) and y-intercept.
Please provide the values based on the graph to finalize the equations. However, as placeholders until further details arise:
- The equation of the solid line is \( y = x \).
- The equation of the dotted line is \( y = mx + c \) where you would need to fill in \( m \) and \( c \). For example, if the slope is 2 and the y-intercept is 1, it would be \( y = 2x + 1 \).
Let me know if there are any specific points on the graph we can work with to derive the correct equations!
1 answer