Find the equation of the linear function represented by the table below in slope-intercept form.
x y
1 1
2 3
3 5
4 7
To find the equation of the linear function in slope-intercept form, we need to find the slope and y-intercept.
We can find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Let's take the first two points (1, 1) and (2, 3):
m = (3 - 1) / (2 - 1)
m = 2 / 1
m = 2
Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the function:
y - y1 = m(x - x1)
Using the first point (1, 1):
y - 1 = 2(x - 1)
Now we can simplify the equation:
y - 1 = 2x - 2
Finally, we can rewrite the equation in slope-intercept form (y = mx + b) by isolating y:
y = 2x - 2 + 1
y = 2x - 1
Therefore, the equation of the linear function is y = 2x - 1.