The equation of the linear function represented by the table is
y = -x + 9
Step-by-step explanation:
The equation of a linear function is y = m x + b, where m is the slope
and b is the y-intercept
To find the equation:
- Use any two points from the table to find the slope m
- Substitute x and y in the equation by the coordinates of any point in the table to find b
The formula of the slope is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] , where
[tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] are two points in the table
The table:
x → -5 -2 1 4
y → 14 11 8 5
Let us use points (-5 , 14) and (-2 , 11) to find the slope of the equation
∵ [tex]x_{1}[/tex] = -5 and [tex]x_{2}[/tex] = -2
∵ [tex]y_{1}[/tex] = 14 and [tex]y_{2}[/tex] = 11
∴ [tex]m=\frac{11-14}{-2--5}=\frac{-3}{3}[/tex]
∴ m = -1
∵ The form of the equation is y = mx + b
- Substitute the value of m in the form
∴ y = -x + b
- To find b substitute x by -5 and y by 14
∴ 14 = -(-5) + b
∴ 14 = 5 + b
- Subtract 5 from both sides
∴ 9 = b
- Substitute the value of b in the equation
∴ y = -x + 9
The equation of the linear function represented by the table is
y = -x + 9
Learn more:
You can learn more about the linear equation in brainly.com/question/9801816
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