Final answer:
The slope of line MN is -0.75 and the product of ( -3s + 2t)(4s - t) is a) ( -22s + 7t ).
Step-by-step explanation:
The slope of a line can be found using the formula: slope = (change in y)/(change in x). Let's calculate the slope of line MN using the given points M(1, 3) and N(5, 0).
To find the change in y, subtract the y-coordinate of one point from the y-coordinate of the other: 0 - 3 = -3.
To find the change in x, subtract the x-coordinate of one point from the x-coordinate of the other: 5 - 1 = 4.
Therefore, the slope of line MN is (-3)/(4) = -0.75.
To find the product ( -3s + 2t)(4s - t), we use the distributive property.
The product is equal to -3s * 4s + (-3s) * (-t) + 2t * 4s + 2t * (-t).
Simplifying, we get -12s² + 3st + 8st - 2t² = -12s² + 11st - 2t².
Therefore, the correct answer is option a: Slope of MN: -0.75, Product: ( -22s + 7t ).