Find the equation of the linear function represented by the table below in slope-intercept form. x: 1 2 3 4 y: -2 -5 -8 -11

Answer 1

To find the equation of the linear function represented by the table, we need to find the slope and y-intercept.

Using two points from the table, we can find the slope (m) using the formula:

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

Let's use the points (1, -2) and (2, -5):

m = (-5 - (-2)) / (2 - 1)
= (-5 + 2) / (2 - 1)
= -3 / 1
= -3

Now that we have the slope, we can use the point-slope form of a linear equation:

y - y1 = m(x - x1)

Using the point (1, -2):

y - (-2) = -3(x - 1)
y + 2 = -3x + 3

To write the equation in slope-intercept form (y = mx + b), we can solve for y:

y = -3x + 3 - 2
y = -3x + 1

Therefore, the equation of the linear function represented by the table in slope-intercept form is y = -3x + 1.