Find the equation of the linear function represented by the table below in slope-intercept form.x01234y27121722

The equation of the function represented by the table is y = 5 x + 2Step-by-step explanation:The equation of the linear function in the slope-intercept form isy = m x + b, wherem is the slope of the lineThe 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_{1},y_{1})[/tex] are any two points lie on the lineb is the y-intercept, means the line intersects the y-axis at point (0 , b)The table:→  x  :    0    :    1    :    2    :    3    :    4→  y  :    2    :    7    :    12  :    17   :    22Let 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 = 5Substitute 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 + 2The equation of the function represented by the table is y = 5 x + 2Learn more:You can learn more about linear function in brainly.com/question/9801816#LearnwithBrainly