Question

Find the equation of the linear function represented by the table below in slope intercept form x 0,1,2,3,4 y -5,2,9,16,23

Answer 1

To find the equation of the linear function represented by the table, we can use the slope-intercept form, which is given by:

y = mx + b

where "m" represents the slope and "b" represents the y-intercept.

To find the slope, we need to calculate the difference in y-coordinates (Δy) divided by the difference in x-coordinates (Δx) for any two points in the table:

m = (y2 - y1)/(x2 - x1)

Taking the points (0, -5) and (1, 2):

m = (2 - (-5))/(1 - 0)
= 7/1
= 7

So, the slope of the linear function is 7.

Now, we can use the slope-intercept form and the y-coordinate of any point to find the y-intercept.

Using the point (0, -5):

-5 = 7(0) + b
-5 = b

Therefore, the y-intercept is -5.

Plugging the slope (m) and the y-intercept (b) into the slope-intercept form:

y = 7x - 5

Hence, the equation of the linear function represented by the table in slope-intercept form is y = 7x - 5.