Answer:
Step-by-step explanation:
x y Difference [tex](y_2-y_1)[/tex]
1 15 -
2 25 25 - 15 = 10
3 35 35 - 25 = 10
4 45 45 - 35 = 10
There is a common difference of 10 in each successive term of y.
Therefore, table represents a linear function.
Let the equation of the linear function is,
y = mx + b
Here 'm' = slope of the line
b = y-intercept
Since, two points (1, 15) and (2, 25) lie on the graph of the function,
Slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m = [tex]\frac{25-15}{2-1}[/tex]
m = 10
Equation of the line will be,
y = 10x + b
For the value of 'b' (y-intercept),
Since, (1, 15) lies on the graph of the linear function,
15 = 10(1) + b
b = 15 - 10
b = 5
Equation of the line on the graph will be,
y = 10x + 5
Now we can determine the output value of the function with the input values, x = 5, 6 and 7
[tex]y_1[/tex] = 10(5) + 5 = 55
[tex]y_2[/tex] = 10(6) + 5 = 65
[tex]y_3[/tex] = 10(7) + 5 = 75
