Straight line LM has equation y = 4x - 7
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Straight line ST has equation y = (9 - x) / 4
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Are the lines LM and ST perpendicular? Yes or No.
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Give a reason for your answer.

To determine if two lines are perpendicular, we need to compare their gradients. Two lines with gradients m₁ and m₂ are perpendicular if and only if their product is -1 (m₁ × m₂ = -1). **1. Gradient of line LM:** The equation is y = 4x - 7. This is in the form y = mx + c, where m is the gradient. So, the gradient of LM is m₁ = 4. **2. Gradient of line ST:** The equation is y = (9 - x) / 4. We need to rewrite this in the form y = mx + c. y = 9/4 - x/4 y = (-1/4)x + 9/4 So, the gradient of ST is m₂ = -1/4. **3. Check the product of the gradients:** m₁ × m₂ = 4 × (-1/4) = -4/4 = -1 Since the product of the gradients is -1, the lines LM and ST are perpendicular. So, the answer is **Yes**.