Find the equation of the linear function represented by the table below in slope-intercept form.x y1 -62 -113 -164 -21

To find the equation of the linear function represented by the table, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.

Step 1: Calculate the slope (m) To find the slope, we can choose any two points from the table. Let's choose the points (1, -6) and (4, -21).

The formula for calculating the slope (m) is: m = (y2 - y1) / (x2 - x1)

Using the coordinates (1, -6) and (4, -21), we can substitute the values into the formula: m = (-21 - (-6)) / (4 - 1) m = (-21 + 6) / (4 - 1) m = -15 / 3 m = -5

So, the slope (m) is -5.

Step 2: Find the y-intercept (b) To find the y-intercept, we can choose any point from the table. Let's choose the point (1, -6).

Using the slope-intercept form of a linear equation (y = mx + b), we can substitute the values of the slope (m) and the coordinates (x, y) into the equation: -6 = -5(1) + b

Simplifying the equation: -6 = -5 + b

To isolate b, we can add 5 to both sides of the equation: -6 + 5 = b -1 = b

So, the y-intercept (b) is -1.

Step 3: Write the equation in slope-intercept form Now that we have the slope (m) and the y-intercept (b), we can write the equation in slope-intercept form (y = mx + b): y = -5x - 1

Therefore, the equation of the linear function represented by the table in slope-intercept form is y = -5x - 1.