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y = -2x + 3

Step-by-step explanation:

We can write an equation in slope-intercept form. Use the slope formula to find the rate of change in the table:

Plug in values from the table:

Simplify:

m = -2 (rate of change)

Use a point from the table (-2, 7) and the slope to solve for the equation for the linear function:

7 = -2(-2) + b

7 = 4 + b

7 -4 = b

b = 3

Rewrite:

y = -2x + 3 is the equation for the linear function.

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)