Find the equation of the linear function represented by the table below in slope-intercept form.
x: 1 2 3 4
y: 6 9 12 15
To find the equation of a linear function in slope-intercept form (y = mx + b), we need to find the values of the slope (m) and y-intercept (b).
First, let's find the slope (m) using the formula:
m = (change in y) / (change in x)
For the given table, we have:
change in x = 2 - 1 = 1
change in y = 9 - 6 = 3
So, the slope (m) is:
m = 3/1 = 3
Next, let's find the y-intercept (b) by substituting one of the given points (x, y) into the slope-intercept form equation: y = mx + b.
Using the point (1, 6), we have:
6 = 3(1) + b
6 = 3 + b
b = 6 - 3
b = 3
Therefore, the equation of the linear function in slope-intercept form is:
y = 3x + 3
this is wrong
Apologies for the incorrect response.
To find the equation of the linear function, we first need to determine the slope (m). We can do this by finding the change in y divided by the change in x:
m = (change in y) / (change in x)
Using the given table, we have:
change in x = 2 - 1 = 1
change in y = 9 - 6 = 3
So, the slope (m) is:
m = 3 / 1 = 3
Now, we need to find the y-intercept (b). The y-intercept is the value of y when x equals 0. We can determine this by substituting one of the given points into the equation y = mx + b.
Using the point (1, 6):
6 = 3(1) + b
6 = 3 + b
b = 6 - 3
b = 3
Therefore, the equation of the linear function in slope-intercept form is:
y = 3x + 3