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Answer :
Final answer:
To determine which points lie on the line represented by the equation y = −4x + 170, substitute the x-values from each point into the equation. The points with the corresponding y-values that match the results of the equation, in this case, points A (0, 170), C (12, 126), and E (5, 150), are on the line.
Explanation:
The given linear equation, y = −4x + 170, allows us to determine which points lie on the line by plugging the x-value of each point into the equation and checking if the resulting y-value matches the one given in the point. To verify each point, follow these steps:
- Substitute the x-value of the point into the equation.
- Calculate the resulting y-value.
- Check if this calculated y-value matches the y-value of the point.
Let's apply these steps to confirm which points are located on the line:
- Point A (0, 170): When x=0, y = −4(0) + 170 = 170, so point A is on the line.
- Point C (12, 126): When x=12, y = −4(12) + 170 = 126, so point C is on the line.
- Point E (5, 150): When x=5, y = −4(5) + 170 = 150, so point E is on the line.
For the other points, either the y-value does not match when we substitute their x-value into the equation, or the y-value is negative which would not make sense in this context since we're measuring something physical like water level.
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