Find the equation of the linear function represented by the table below in slope-intercept form.
x y
1 6
2 11
3 16
4 21
To find the equation of the linear function represented by the table, note that the y-values increase by 5 for each increase of 1 in the x-values. This indicates that the slope of the linear function is 5.
Using the point-slope form of a linear equation, we can choose any point on the line to substitute into the slope-intercept form. Let's use the point (1, 6).
The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.
Since the slope is 5 and the point (1, 6) lies on the line, we can substitute these values into the equation to find the y-intercept:
6 = 5(1) + b
Simplifying this equation, we get:
6 = 5 + b
Subtracting 5 from both sides, we get:
b = 1
Therefore, the equation of the linear function represented by the table in slope-intercept form is:
y = 5x + 1.