The linear equation is y = -2 x + 198
Jeff’s weight after 12 weeks is 174 pounds
Step-by-step explanation:
Jeff is keeping Trace of his weight over several weeks
We need to write a linear equation represents the Jeff’s weight, and find his weight after 12 weeks
The form of the linear equation is y = mx + b, where m is the slope of the line, and b is the y-intercept
The formula of the slope of a line which passes through points [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Let y represents Jeff's weight in x weeks
∵ After 2 weeks, he weighs 194 pounds
∴ [tex](x_{1},y_{1})[/tex] = (2 , 194)
∵ After 6 weeks , he weighs 186 pounds
∴ [tex](x_{2},y_{2})[/tex] = (6 , 186)
- Use these two points to find m
∵ [tex]m=\frac{186-194}{6-2}=\frac{-8}{4}=-2[/tex]
∴ m = -2
- Substitute the value of m in the form of the equation
∴ y = -2 x + b
- To find b substitute x and y in the equation by the coordinates
of any point on the line
∵ x = 2 and y = 194
∴ 194 = -2(2) + b
∴ 194 = -4 + b
- Add 4 to both sides
∴ 198 = b
∴ y = -2 x + 198
The linear equation is y = -2 x + 198
To find his weight after 12 weeks substitute x by 12 in the equation
∵ x = 12
∴ y = -2(12) + 198
∴ y = -24 + 198
∴ y = 174
Jeff’s weight after 12 weeks is 174 pounds
Learn more:
You can learn more about the linear equations in brainly.com/question/4819659
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