Question
X-11,20. Y-58,103. Write the equation of the linear function that models the relationship shown in the table. Enter your answer in y=MX+b form.
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GPT 3.5
To find the equation of the linear function, we can find the slope (M) and the y-intercept (b) using the given coordinates.
The slope (M) can be calculated using the formula:
M = (Y₂ - Y₁) / (X₂ - X₁)
Plugging in the values, we have:
M = (103 - 58) / (20 - 11)
M = 45 / 9
M = 5
The y-intercept (b) is the value of y when x = 0. We can find it by substituting any of the given points (x, y) into the equation:
Y = MX + b
103 = (5)(20) + b
103 = 100 + b
b = 103 - 100
b = 3
Therefore, the equation of the linear function that models the relationship shown in the table is:
y = 5x + 3
The slope (M) can be calculated using the formula:
M = (Y₂ - Y₁) / (X₂ - X₁)
Plugging in the values, we have:
M = (103 - 58) / (20 - 11)
M = 45 / 9
M = 5
The y-intercept (b) is the value of y when x = 0. We can find it by substituting any of the given points (x, y) into the equation:
Y = MX + b
103 = (5)(20) + b
103 = 100 + b
b = 103 - 100
b = 3
Therefore, the equation of the linear function that models the relationship shown in the table is:
y = 5x + 3
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