Find the equation of the linear function represented by the table below in slope-intercept form.
x: -1 2 5 8
y: 0 15 30 45
To find the equation of the linear function in slope-intercept form (y = mx + b), we need to find the slope (m) and the y-intercept (b).
To find the slope (m), we can use the formula:
m = (change in y) / (change in x)
Let's find the change in y and change in x for two points in the table:
For the points (-1, 0) and (2, 15),
change in y = 15 - 0 = 15
change in x = 2 - (-1) = 2 + 1 = 3
m = 15/3 = 5
Now, we have the slope (m) as 5.
To find the y-intercept (b), we can use the formula:
b = y - mx
Let's use the first point (-1, 0) to find the y-intercept:
0 = -1(5) + b
0 = -5 + b
b = 5
Now, we have the slope (m) as 5 and the y-intercept (b) as 5.
Therefore, the equation of the linear function represented by the table is:
y = 5x + 5