The equation of the function represented by the table is y = 5 x + 2
Step-by-step explanation:
The equation of the linear function in the slope-intercept form is
y = m x + b, where
The table:
→ x : 0 : 1 : 2 : 3 : 4
→ y : 2 : 7 : 12 : 17 : 22
Let us chose any two points from the table to calculate the slope
∵ Points (1 , 7) and (2 , 12) lie on the line
∴ [tex]x_{1}[/tex] = 1 and [tex]x_{2}[/tex] = 2
∴ [tex]y_{1}[/tex] = 7 and [tex]y_{2}[/tex] = 12
- Substitute these values in the formula of the slope
∵ [tex]m=\frac{12-7}{2-1}=\frac{5}{1}[/tex]
∴ m = 5
Substitute the value of m in the form of the equation
∵ y = m x + b
∴ y = 5 x + b
∵ The line intersects the y-axis at point (0 , b)
∵ From the table point (0 , 2) lies on the line
∴ b = 2
∴ y = 5 x + 2
The equation of the function represented by the table is y = 5 x + 2
Learn more:
You can learn more about linear function in brainly.com/question/9801816
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