Question

jeff is keeping track of his weight over several weeks. After 2 weeks, he weighs 194 pounds. After 6 weeks, he weighs 186 pounds. write and solve a linear equation to find jeffs weight after 12 weeks

Answer 1

y = -2x + 198

174 pounds

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Establish a linear equation based on the information provided

We know that Jeff's weight after 2 weeks is 194 pounds and after 6 weeks is 186 pounds. This gives us two points:

• (2, 194) and (6, 186)

Calculate the slope (m)

Use the slope formula:

• (y₂ - y₁) / (x₂ - x₁), where (x₁, y₁) and (x₂, y₂) are points on the line.

Plug in values:

• m = (186 - 194) / (6 - 2) = -8 / 4 = -2

Use one point to solve for the y-intercept (b)

Substitute the slope and one point into the slope-intercept form, y = mx + b:

• 194 = (-2)(2) + b
• b = 194 + 4 = 198

Write the linear equation

Now we can formulate the equation:

• y = -2x + 198

Solve for Jeff's weight after 12 weeks

Substitute x = 12 into the equation:

• y = -2(12) + 198
• y = -24 + 198 = 174

Jeff's predicted weight after 12 weeks is 174 pounds.