use the graph below to answer the question
(4,10.5)
(7,15.75)
(3,8.75)
(6,14)
If the table of values represents a linear function, write the equation of the linear function:
y=
To find the equation of the linear function, we need to find the slope (m) and the y-intercept (b).
Slope formula: m = (change in y) / (change in x)
Using the points (4, 10.5) and (7, 15.75):
m = (15.75 - 10.5) / (7 - 4)
m = 5.25 / 3
m = 1.75
Substituting the slope into the slope-intercept form: y = mx + b
We can substitute one of the points into the equation to solve for b.
Using the point (4, 10.5):
10.5 = 1.75(4) + b
10.5 = 7 + b
10.5 - 7 = b
3.5 = b
Therefore, the equation of the linear function is:
y = 1.75x + 3.5