Find the equation of the linear function represented by the table below in slope-intercept form. x y 1 7 2 10 3 13 4 16
The given table represents a linear function. To find the equation of this linear function in slope-intercept form (y = mx + b), we need to first find the slope (m) and the y-intercept (b).
To find the slope, we can use any two points from the table. Let's use the first and last points: (1, 7) and (4, 16).
The slope (m) is given by the formula: m = (change in y) / (change in x).
Change in y = 16 - 7 = 9,
Change in x = 4 - 1 = 3.
So, the slope (m) = 9/3 = 3.
Now, let's find the y-intercept (b) by substituting the slope (m) and any point (x, y) from the table into the slope-intercept form equation: y = mx + b.
Using the point (1, 7):
7 = 3(1) + b
7 = 3 + b
b = 7 - 3
b = 4.
Therefore, the slope (m) is 3 and the y-intercept (b) is 4.
The equation of the linear function represented by the table in slope-intercept form is:
y = 3x + 4.