The equation you're working with is \( y = -0.14x + 3 \). It represents a linear function with a slope of \(-0.14\) and a y-intercept of \(3\).
If you change the constant term from \(3\) to \(0\), the new equation will be:
\[ y = -0.14x + 0 \quad \text{or simply} \quad y = -0.14x \]
Effect on the Graph:
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Y-Intercept: The original graph had a y-intercept of \(3\) (the point where the line crosses the y-axis). By changing it to \(0\), the new line will pass through the origin \((0, 0)\).
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Slope: The slope remains the same at \(-0.14\). So, the slope of the line is still the same steepness, and it still decreases as you move from left to right (since the slope is negative).
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Points of Intersection:
- The original graph intersects the y-axis at \((0, 3)\) and intersects the x-axis at the point where \(y=0\): \[ 0 = -0.14x + 3 \quad \Rightarrow \quad 0.14x = 3 \quad \Rightarrow \quad x \approx 21.43 \] Thus the x-intercept is approximately \((21.43, 0)\).
- The new graph will still have the same slope and will intersect the x-axis at: \[ 0 = -0.14x \quad \Rightarrow \quad x = 0 \] Since the line now passes through the origin, it will intersect the x-axis at \((0, 0)\).
Summary:
- The new graph \( y = -0.14x + 0 \) will shift downwards, moving the y-intercept from \(3\) to \(0\) and intersecting the y-axis at the origin.
- The line will be the same angle in terms of slope, but it will effectively lower the entire line, eliminating the intercept at \((0, 3)\) and moving it through the origin.
Here's how it will visually look:
- Original line: intercepts at \((0, 3)\) and \((21.43, 0)\)
- New line: intercepts at \((0, 0)\) and will have the same general slope, going downward as \(x\) increases.